# A Sustainable Economic System to Face the Fluctuation of Fruit Prices: Based on a Small-Region DSGE Model

Authors: Hailing Fu; Yuantao Fang; Yi Qu; Yi Pan
Journal: Discrete Dynamics in Nature and Society
 (2021)

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## Abstract

This paper builds a new small-scale and regionalization DSGE model that focuses on the sustainable economic system, which was estimated by the Bayesian estimation method using Chinese annual data from 2004 to 2017 to analyze the effect of the fluctuation of fruit prices in Hainan. We find the fluctuation of increasing prices has a negative effect on fruit output. This results in a preference to loosen monetary policy to reduce this influence and then results in price inflation, which will lead to the increase in output and prices simultaneously. Based on our findings, we provide suggestions for policy maker such as the optimization of industrial structures and increased investment in the fruit industry, extending the fruit industry chain and establishing a multifruit industry sustainable economic system.


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## Body

## 1. Introduction

Fruit is an important economic crop in China and plays a large role in the national economy. According to FAOSTAT, compared to the rest of the world, China’s fruit planting area and output have been consistently number one, and each year, over 675 million metric tons of fruit is produced worldwide. “Early Harvest Program” of the China-ASEAN Free Trade Area (CAFTA) was launched, realizing the market opening of agricultural products. China had eliminated import tariffs on about 600 agricultural products between China and ASEAN’s major members, and also the zero-tariff policies have been implemented on tropical fruits in the region. Since the implementation of the plan, bilateral trade in agricultural products has grown rapidly. Meanwhile, on November 15, 2020, the 4th Regional Comprehensive Economic Partnership (RCEP) Leaders’ Meeting was held. After the meeting, the 10 ASEAN countries and 15 Asia-Pacific countries including China and Japan formally signed “Regional Comprehensive Economic Partnership Agreement.” Signing the agreement marks the official start of the free trade zone with the largest population, the largest economic and trade scale, and the most development potential in the world. It promotes the development of China’s tropical fruit processing industry, but it also has a great impact on the tropical fruit industry with Chinese characteristics, which complicates the adjustment and optimization of China’s tropical fruit industrial structure. As one of the most important consumer goods, the price of fruit is high and fluctuating, which has a devastating effect on developing countries and the world’s poor populations [1]. Therefore, it is a serious task to reform traditional agriculture, fine-tune tropical fruit industry structure with Chinese characteristics, increase farmers’ income, and promote sustainable and healthy agricultural development.Hainan is an important area for the development of tropical agriculture in China. It is located at the northern latitude 18°10′–20°10′ and eastern longitude 108°37′–111°03′ with 33,920 square kilometers (13,100 sq. mi) of tropical area. It has precipitation of 1437.0–3022.7 mm, 23.4–26.5°C average temperature, and 1573.5–2443.4 hours of annual daylight. This makes it a suitable place for tropical fruit production. The tropical fruit industry is an important part of the Hainan economy system. Table1 shows the annual tropical fruit farming GDP of Hainan province from 2010 to 2019, 4% to 5% of the entire GDP of Hainan on average. Hainan’s tropical fruit production not only supplies other provinces, but also the tropical fruit industry is becoming more and more important to the Hainan economy.Table 1
Annual fruit GDP of Hainan province from 2010 to 2019.
Year2010201120122013201420152016201720182019Fruit GDP12019110881060812388150021578418263202322017825654% of GDP5.82%4.40%3.71%3.90%4.29%4.26%4.52%4.53%4.18%4.83%Unit: million RMB, Source: Statistical Yearbook of Hainan Province and National Bureau of Statistics of China.However, due to the nature of fruit and economic factors, fruit prices are inevitably faced with the dual pressures of natural risks and market risks. As Ma and Sun [2] proposed, with the expansion of the price adjustment parameter, the economic system shows a wealth of complex features and enters the chaos period. The long production cycle and the time between the production decisions and market sales, and the lag in time taken for the adjustment of market prices to production, directly lead to fruit price fluctuations. The fluctuation of the fruit price affects the entire fruit industry and the total GDP growth. This results in economic policies reducing the relevant negative influences and ensuring healthy economic growth. The research of Wandong Lou and Junhai Ma [3] shows that the adjustments of price would affect the stability and profits much more than the sales effort in economic system. They proposed that every supply chain should take the suitable adjustment speeds for the price to keep the system in the stable state.The current research aims at tropical fruits of Hainan to analyze the effect of the fluctuation of fruit price on its economic system. This kind of economic system has the characteristics of small scale and regionalization. Based on the researches of Ireland [4] and Smets and Wouters [5], from the side of supply-side structural reform, we build a small-scale, regionalization, and specialized DSGE model estimated by the maximum likelihood method using annual Chinese data from 2004 to 2017, with the purpose of developing a sustainable economic system of tropical fruit industry in Hainan.This study contributes three innovations to the scientific literature. Firstly, it adds a fruit variable into consumption and production as raw materials for consumer goods and intermediate products, respectively. Secondly, under the framework of dynamic stochastic general equilibrium (DSGE), this paper divides fruit into fruit consumer goods and fruit production raw materials in the household sector and the manufacturing sector, respectively. At the same time, the fruit price also enters the optimization problem of representative households and companies in the form of random variables. This is to study the dynamic impact of fruit price shocks on Hainan’s macroeconomy. We also add fruit price shocks to investigate the impact on various variables in Hainan’s economy. Thirdly, the model consists of representative households and representative companies; among them, the family consumes two types of consumer goods: fruit consumer goods and non-fruit consumer goods. Simultaneously, it also provides labor and private capital to manufacturers for remuneration and capital rent, while manufacturers make use of labor, capital, and fruit-based raw materials for production.In the next section, we review the relevant literatures. The rest of the paper is as follows. Section3 discusses the general model of this study. Section 4 presents the data and the analysis of the model results. Finally, Section 5 provides conclusions, policy suggestions, and possible future research directions.


## 2. Literature Review

Economists and central banks frequently use DSGE models to analyze macroeconomies and to evaluate economic policy [6]. During the past decade, DSGE models have been gaining popularity and become the standard framework for monetary policy, economic fluctuation, and economic forecasting. Studies have been made on economies of different levels of development. Kang and Suh [7] researched the influence of the global financial crisis and labor markets on GDP growth through a DSGE model sample of the more advanced economy of South Korea. Pop [8] used a DSGE model to analyze the relation between inflation and monetary policy in Romania, an emerging economy. Bondzie et al. [9] studied the oil price fluctuations and the relevant influence on the economic growth based on a DSGE approach. Smets and Wouters [10] investigated the business cycle of US economy and estimated a DEGE model using Bayesian methods [11, 12]. Meanwhile, DSGE models have particularly been employed in the research literature on China’s economic growth and development. Different types of DSGE models have been developed and applied by researchers in diverse studies. He et al. [13] found that the housing market shocks, such as the housing preference shocks and the loan-to-value ratio, influence the macroeconomy of China based on DSGE analysis. Mehrotra et al. [14] focused on the costs in capital adjustment, habit formation in consumption, and price rigidities, developing a small-scale DSGE model to explore the impact of Chinese economic rebalancing after responding to different shocks. Miao and Peng [15] applied the new Keynesian DSGE model to explore the root of business cycles in China and noted that inflation, productivity, and credit shocks are the three driving forces of the economic fluctuations in China. Jia et al. [16], by developing an open economy model, researched the shocks for the trade-offs on the fiscal and monetary policy aspects.Due to China’s unique institutional structure, different aspects of rule-based DSGE frameworks have gradually become more popular in the study of China’s macroeconomic policy. Until now, however, there is no consensus on which kind of rule is better in DSGE frameworks to characterize China’s macroeconomic policy. Kenichi Tamegawa [6] pointed out that small regions’ policy makers need an effective small-region DSGE model to evaluate their policies, or they will be forced to use traditional macroeconomy models. Because the Hainan economic system has the characteristics of small-scale and regionalization, we try to develop a small-region DSGE model to research it.Fruit price mainly affects the macroeconomy in two ways. First, from the aspect of supply, the rise of fruit prices leads to the rise of purchasing costs of related companies, which in turn leads to a decrease of output and the slowdown of economic growth. At the same time, it also causes the emergence of industrial structure adjustment, and structural unemployment appears, and macroeconomic prosperity declines. Second, from the demand side, the rise of fruit prices raises overall inflation, which in turn leads to a decrease in real income of citizens and a decrease in total consumption. At the same time, rising fruit prices can also cause reduced citizens’ demand for fruit-based consumer goods, reduced risk appetite, and increased “cautious saving.” Therefore, the price is the main factor affecting supply and demand. The demand–supply evolution is periodic as the provider alternates between cultivating and exploiting the herd effect [17].The existing notable studies almost solely focus on the entire country’s economy. There is limited study on the special tropical agriculture province of China. In this paper, for our research, we concentrate on Hainan Province through the new small-scale, regionalization, and specialized DSGE model estimated by the maximum likelihood method using Chinese yearly data of 2004–2017 to analyze the effect of the fluctuation of fruit price on its economy.


## 3. General Model

Our benchmark model economy, which is a slightly modified version taken from Liu and Song [18], consists of the representative household, finished goods-producing firm, intermediate goods producing firm, and central bank.As shown in Figure1, households provide capital to intermediate goods producing companies and receive labor income, which is divided into two parts: one part is investment, and the other part is consumption. Consumption of goods includes two kinds: fruit goods and non-fruit goods. Intermediate goods producing companies will use fruit, capital, and labor to produce intermediate goods while maximizing profit and then sell these intermediate goods to finished goods-producing companies. Note that fruit, as part of final goods, will be used to produce intermediate goods and consumed by households.Figure 1
The basic structure of model.


### 3.1. Representative Household

Assume that the representative household enters each time periodt = 0,1,2,3, …by maximizing the utility function:(1)E0∑t=0∞βtUCtkFth1−k,MtPt,ht,where β is discount factor and 0 < β < 1, meaning that the representative household pursues the maximization of the lifetime utility present value.Spot utility function of the representative household:(2)UCtkFth1−k,MtPt,ht=atCtkFtk1−k1−σc1−σc+Mt/Pt1−σm1−σc−ht1+σ21+σ2,where Ct is the nonfruit consumption of goods; Fth is the fruit consumption of goods; ht is the labor supply; Mt is the money held at the end of time t; σc,σm and σL are all greater than 0, and 1/σc, 1/σm and 1/σL represent the intertemporal substitution elasticity of consumption, the interest rate elasticity of money demand, and the Frisch elasticity of labor supply.The preference shock of consumption is as follows:(3)lnat=1−θalna+θalnat−1+εta,where 0 ≤ δa ≤ 1.εta follows a normal distribution with mean 0 and variance σa2.The intertemporal budget constraint faced by the representative household for the periodst = 0, 1, Z, …, n is(4)wtht+Bt−1+Tt+Mt−1+Dt+RtkKt−1≥PtCt+Pt0Ft+Btrt+Mt,where Bt is the total bond at the end of time t; wt is the nominal wage rate for the time period; Tt is the transfer payment; Mt − 1 is the money holding with a lag of one period; RtkKt−1 is the nominal income from capital rental. At the end of the period t, the household receives a nominal profit share Dt=∫01Dt2di (2)di from the intermediate goods producing companies i∈0,1, where Dt(i) is the profit earned from the company i at the time period t.Capital function:(5)Kt=1−θKt−1+1−Sxtitit−1it,where θ is the capital depreciation rate, and s is the cost of capital adjustment with s′=0. Xt is the capital adjustment cost shock with(6)LnXt=1−θxlnX+θxlnXt−1+εtX,where 0 ≤ θx < 1 and εtxfollows normal distribution with mean 0 and variance σx2.We assume in this model that the labor supply is heterogeneous, and the household is the price maker. We use the sticky prices assumption of Wu, and Chang [19]. At the end of time t, only (1 − ξw) households could get the best price, while other households adjust price according to the last period, which is(7)Wtj=πt−1Wt−1j.Assume that the labor supply market has a perfect system, and the market could adjust itself to get the maximum profit, which decides the best amount of each kind of labor j:(8)MaxWtht−∫01Wtjhtjdj,where Wt is the nominal wage, and Wt(j) is the wage level of household j, while htj represents the labor demand of household j.The total labor demand:(9)ht=∫01htjθtw−1/θtwdjθtw/θtw−1,where θtw is the wage elasticity of the labor demand.When the market reaches equilibrium, the profit of total labor supply is zero; thus, we get(10)Wt=∫01Wj1−θtwdj1/1−θtw=ξwπt−1Wt−11−θtw+1−εww¯t1−θtw1/1−θtw.Defineγt+kw=θtw/θtw−1, and then wage plus shock is γt+kw(11)lnγtw=1−θywlnγ+θywlnγt−1w+εtγw,where 0 ≤θyw<1 and εtγw follows normal distribution with mean 0 and variance σγw2.


### 3.2. Finished Goods-Producing Company

According to Ireland [4], the finished goods-producing company buys Yti i∈[0,1] units of the intermediate goods at the price Pti to produce Yt units of the finished goods using the constant-return-to-scale technology described by(12)∫01Ytiθtp−1/θtpdiθtp/θtp−1,where θt is the elasticity of demand for the intermediate goods, which follows the autoregressive process:(13)lnθtp=1−ρθlnθ¯+ρθlnθt−1p+εθt,where θ¯>1 and 1 >θtp ≥ 0.As the finished goods-producing firms face perfect competition capital and goods markets, each firm will decide to maximize its profit givenPti and Pt, which leads to the demand of intermediate goods:(14)Yti=PtiPt−θtpYt.As for intermediate goods,θtp is the same. Competition will lead to the zero profit of the finished goods-producing company, which will decide Pt as follows:(15)Pt=∫01Pti1−θtpdi.


### 3.3. Intermediate Goods-Producing Companies

Assume that all firms have infinite life and distribute continuously [0,1]. We consider the intermediate goods-producing firmi who uses labor, capital, and original fruit to produce goods by the Cobb–Douglas function.(16)Yti=zthti∂1kt−1i∂2Ftfi∂3,where∂1, ∂2 and ∂3 are all greater than 0 and ∂1 + ∂2 + ∂3  = 1. Zt is the technology shock as follows:(17)lnZt=1−δzlnZ+δzlnZt−1+εtz,where 0≤δz<1 and z>0. εtz follows normal distribution with mean 0 and variance σz2.The company faces a perfect competition input demand market. It can hireht unit labor with fixed price Wt, rent kt − 1 unit capital with fixed rent rate Rtk and buy Ftf original fruit with fixed price Ptf to produce γt(i) intermediate-producing goods. The cost function is as follows:(18)Cti=RtkKt−1i+Wthti+PtfFtf.Assume that the fruit price is as follows:(19)lnPtf=1−δpflnPf+δpflnPt−1f+εtpf,where 1≥δpf≥0, Pf>0 and εtpf∼N(0, δpf2).The marginal costCti/yti=1/Zt∂1−∂1∂2−∂2∂3−∂3Wt∂1r1k∂2ptf∂3, is related to the technology level and input price, which is suitable for all intermediate goods-producing companies.We use the sticky prices assumption of Calvo [20]. As adjusting price will affect the preference of consumers and increase the management cost, firms can only adjust it cyclically. Assume that, for each period, only (1 − ξp) intermediate goods-producing companies could get the best price to sell goods and other companies adjust price according to the last period as follows:(20)Pti=EtπtPt−1i,(21)Etπt=πttargzπt−11−z,where πt−1=Pt−1/Pt−2 represents the measurable inflation of the last period.πttarg is the target inflation of the central bank, which is assumed to be equal to the stable value of inflation.Defineγt+kp=θtp/θtp−1, and then price plus shock is as follows:(22)lnγtp=1−θγplnγ+θγplnγt−1p+εtγp,where 0 ≤θγp<1, and εtγp is a normal distribution with mean 0 and variance σγp2.The total price is as follows:(23)Pt=∫01Pi1−θtσdi1/1−θtσ=ξpπt−1pt−11−θtσ+1−ξppt¯1−θtσ1/1−θtσ.Meanwhile, final goods will be divided into two parts: fruit goods include those used to produce intermediate goods and those consumed by households; non-fruit goods will be consumed and invested by households. Thus, the final goods should be satisfied:(24)Yt=Ct+it+PtfFtf+PtfFth.


### 3.4. Central Bank

The monetary policy model of the central bank refers to Ireland [4], assuming that the central bank corrects the gap between output yt and inflationπt by adjusting the linear combination of short-term nominal interest rate rtand monetary growth rateμt, and the monetary growth rate satisfies(25)μt=MtMt−1.Inflation rate is defined by(26)πt=PtPt−1.According to the rule of monetary policy,(27)lnrtr=ωrlnrt−1r+1−ωrωπlnπtπ+ωylnyty+ωμlnμtr+lnVt,where ωr, ωμ, ωy and ωπ are decided by the central bank; r, μ, y and π are the stead values of rt, μt, yt and πt. When ωμ=0, it becomes the Taylor [21] rule; when lnrt/r=lnrt−1/r=0 and ωπ=0, it is consistent with the policy rule, as the central brand adapts to an increase in the output only by increasing the money supply [22]. Finally, when lnrt/r=lnrt−1/r=0 and ωy=ωπ=0, it is consistent with Rotemberg [23]. The shock of monetary policy vt is as follows:(28)lnVt=1−ρvlnV+ρvlnVt−1+εtv,where. 0≤ρv<1andεtv∼N0,σv2


## 3.1. Representative Household

Assume that the representative household enters each time periodt = 0,1,2,3, …by maximizing the utility function:(1)E0∑t=0∞βtUCtkFth1−k,MtPt,ht,where β is discount factor and 0 < β < 1, meaning that the representative household pursues the maximization of the lifetime utility present value.Spot utility function of the representative household:(2)UCtkFth1−k,MtPt,ht=atCtkFtk1−k1−σc1−σc+Mt/Pt1−σm1−σc−ht1+σ21+σ2,where Ct is the nonfruit consumption of goods; Fth is the fruit consumption of goods; ht is the labor supply; Mt is the money held at the end of time t; σc,σm and σL are all greater than 0, and 1/σc, 1/σm and 1/σL represent the intertemporal substitution elasticity of consumption, the interest rate elasticity of money demand, and the Frisch elasticity of labor supply.The preference shock of consumption is as follows:(3)lnat=1−θalna+θalnat−1+εta,where 0 ≤ δa ≤ 1.εta follows a normal distribution with mean 0 and variance σa2.The intertemporal budget constraint faced by the representative household for the periodst = 0, 1, Z, …, n is(4)wtht+Bt−1+Tt+Mt−1+Dt+RtkKt−1≥PtCt+Pt0Ft+Btrt+Mt,where Bt is the total bond at the end of time t; wt is the nominal wage rate for the time period; Tt is the transfer payment; Mt − 1 is the money holding with a lag of one period; RtkKt−1 is the nominal income from capital rental. At the end of the period t, the household receives a nominal profit share Dt=∫01Dt2di (2)di from the intermediate goods producing companies i∈0,1, where Dt(i) is the profit earned from the company i at the time period t.Capital function:(5)Kt=1−θKt−1+1−Sxtitit−1it,where θ is the capital depreciation rate, and s is the cost of capital adjustment with s′=0. Xt is the capital adjustment cost shock with(6)LnXt=1−θxlnX+θxlnXt−1+εtX,where 0 ≤ θx < 1 and εtxfollows normal distribution with mean 0 and variance σx2.We assume in this model that the labor supply is heterogeneous, and the household is the price maker. We use the sticky prices assumption of Wu, and Chang [19]. At the end of time t, only (1 − ξw) households could get the best price, while other households adjust price according to the last period, which is(7)Wtj=πt−1Wt−1j.Assume that the labor supply market has a perfect system, and the market could adjust itself to get the maximum profit, which decides the best amount of each kind of labor j:(8)MaxWtht−∫01Wtjhtjdj,where Wt is the nominal wage, and Wt(j) is the wage level of household j, while htj represents the labor demand of household j.The total labor demand:(9)ht=∫01htjθtw−1/θtwdjθtw/θtw−1,where θtw is the wage elasticity of the labor demand.When the market reaches equilibrium, the profit of total labor supply is zero; thus, we get(10)Wt=∫01Wj1−θtwdj1/1−θtw=ξwπt−1Wt−11−θtw+1−εww¯t1−θtw1/1−θtw.Defineγt+kw=θtw/θtw−1, and then wage plus shock is γt+kw(11)lnγtw=1−θywlnγ+θywlnγt−1w+εtγw,where 0 ≤θyw<1 and εtγw follows normal distribution with mean 0 and variance σγw2.


## 3.2. Finished Goods-Producing Company

According to Ireland [4], the finished goods-producing company buys Yti i∈[0,1] units of the intermediate goods at the price Pti to produce Yt units of the finished goods using the constant-return-to-scale technology described by(12)∫01Ytiθtp−1/θtpdiθtp/θtp−1,where θt is the elasticity of demand for the intermediate goods, which follows the autoregressive process:(13)lnθtp=1−ρθlnθ¯+ρθlnθt−1p+εθt,where θ¯>1 and 1 >θtp ≥ 0.As the finished goods-producing firms face perfect competition capital and goods markets, each firm will decide to maximize its profit givenPti and Pt, which leads to the demand of intermediate goods:(14)Yti=PtiPt−θtpYt.As for intermediate goods,θtp is the same. Competition will lead to the zero profit of the finished goods-producing company, which will decide Pt as follows:(15)Pt=∫01Pti1−θtpdi.


## 3.3. Intermediate Goods-Producing Companies

Assume that all firms have infinite life and distribute continuously [0,1]. We consider the intermediate goods-producing firmi who uses labor, capital, and original fruit to produce goods by the Cobb–Douglas function.(16)Yti=zthti∂1kt−1i∂2Ftfi∂3,where∂1, ∂2 and ∂3 are all greater than 0 and ∂1 + ∂2 + ∂3  = 1. Zt is the technology shock as follows:(17)lnZt=1−δzlnZ+δzlnZt−1+εtz,where 0≤δz<1 and z>0. εtz follows normal distribution with mean 0 and variance σz2.The company faces a perfect competition input demand market. It can hireht unit labor with fixed price Wt, rent kt − 1 unit capital with fixed rent rate Rtk and buy Ftf original fruit with fixed price Ptf to produce γt(i) intermediate-producing goods. The cost function is as follows:(18)Cti=RtkKt−1i+Wthti+PtfFtf.Assume that the fruit price is as follows:(19)lnPtf=1−δpflnPf+δpflnPt−1f+εtpf,where 1≥δpf≥0, Pf>0 and εtpf∼N(0, δpf2).The marginal costCti/yti=1/Zt∂1−∂1∂2−∂2∂3−∂3Wt∂1r1k∂2ptf∂3, is related to the technology level and input price, which is suitable for all intermediate goods-producing companies.We use the sticky prices assumption of Calvo [20]. As adjusting price will affect the preference of consumers and increase the management cost, firms can only adjust it cyclically. Assume that, for each period, only (1 − ξp) intermediate goods-producing companies could get the best price to sell goods and other companies adjust price according to the last period as follows:(20)Pti=EtπtPt−1i,(21)Etπt=πttargzπt−11−z,where πt−1=Pt−1/Pt−2 represents the measurable inflation of the last period.πttarg is the target inflation of the central bank, which is assumed to be equal to the stable value of inflation.Defineγt+kp=θtp/θtp−1, and then price plus shock is as follows:(22)lnγtp=1−θγplnγ+θγplnγt−1p+εtγp,where 0 ≤θγp<1, and εtγp is a normal distribution with mean 0 and variance σγp2.The total price is as follows:(23)Pt=∫01Pi1−θtσdi1/1−θtσ=ξpπt−1pt−11−θtσ+1−ξppt¯1−θtσ1/1−θtσ.Meanwhile, final goods will be divided into two parts: fruit goods include those used to produce intermediate goods and those consumed by households; non-fruit goods will be consumed and invested by households. Thus, the final goods should be satisfied:(24)Yt=Ct+it+PtfFtf+PtfFth.


## 3.4. Central Bank

The monetary policy model of the central bank refers to Ireland [4], assuming that the central bank corrects the gap between output yt and inflationπt by adjusting the linear combination of short-term nominal interest rate rtand monetary growth rateμt, and the monetary growth rate satisfies(25)μt=MtMt−1.Inflation rate is defined by(26)πt=PtPt−1.According to the rule of monetary policy,(27)lnrtr=ωrlnrt−1r+1−ωrωπlnπtπ+ωylnyty+ωμlnμtr+lnVt,where ωr, ωμ, ωy and ωπ are decided by the central bank; r, μ, y and π are the stead values of rt, μt, yt and πt. When ωμ=0, it becomes the Taylor [21] rule; when lnrt/r=lnrt−1/r=0 and ωπ=0, it is consistent with the policy rule, as the central brand adapts to an increase in the output only by increasing the money supply [22]. Finally, when lnrt/r=lnrt−1/r=0 and ωy=ωπ=0, it is consistent with Rotemberg [23]. The shock of monetary policy vt is as follows:(28)lnVt=1−ρvlnV+ρvlnVt−1+εtv,where. 0≤ρv<1andεtv∼N0,σv2


## 4. Model Results

### 4.1. Data

The data used in this paper is the total output, investment, money supply, wages, inflation, and the percentage change of fruit consumption from state values. The data is from 2004 to 2017. We use GDP and The Total Sales of Consumer Goods as total output in Hainan, Total Investment in Fixed Assets as investment, M2 in Hainan as money supply, and the Total Output of Fruit Production as fruit consumption. The inflation is calculated using CPI in 2004 as the base element.


### 4.2. Parameter Estimation

The parameters in this paper are calculated using two methods. For some fixed parameters, the values are taken from the literature related the Chinese economy. For dynamic parameters, we estimate them using a Bayesian method.The total number of parameters in this paper is 11:β, σL, ζ, δ, ∂1, ∂2, ∂3, σM, εc, εi, εf.β is the discount factor. In China, the interest rate for a one-year deposit is 2.75%; therefore, we get the value of β as 0.973. σL is the rate of labor negative utility. When we assume that the labor supply market is a monopoly competitive market, the value of σL is between 0.3 and 1 [18]. Based on the study by CMR (2007), we set the value of σL to be equal to 1. σM is the rate of monetary utility, based on Tong [24], and we choose 1.4 as the value of σM.δis the capital depreciation rate, which is equal to 10% for one year in this paper as the previous research [19]. ζ represents the monopoly level of the market. ζ can be calculated by the steady-state price addition of θω. Based on Ireland [4], we choose 6 as the value of θω, and then the value of ζ is 1.2, which means that the steady state price plus is 20%.∂1, ∂2 and ∂3 represent the ratio of input during the process of intermediate goods production. Based on Tong [24] calculated the actual data of China by the income approach and developed the value of ∂1 to be 0.6, which means that the labor income accounts for 60% of the total income of intermediate products in the steady state. According to Ireland [4], the assumed value of ∂2is 0.21. Because ∂1 + ∂2 + ∂3 = 1, the calculated value of ∂3 is 0.19.According to the calculation,εc, εi and εf represent the ratio of non-fruit consumption, investment, and fruit consumption to GDP, which are 0.372, 0.528, and 0.1, respectively. Table 2 shows the definitions and the values of fixed parameter.Table 2
Fixed parameter definitions and their values.
ParameterDefinitionValueβDiscount factor0.973σLThe rate of labor negative utility1ζMonopoly level of market1.2δCapital depreciation rate0.01∂1Labor elasticity0.6∂2Capital elasticity0.21∂3Fruit elasticity0.19σMThe rate of monetary utility1.4εcNonfruit consumption to GDP0.372εiInvestment to GDP0.528εfFruit consumption to GDP0.1The number of dynamic parameters in this paper is 24.σc and k are the economic behaviors of representative household, ψ is the investment behaviours, ξw is the wage pricing process, ξp and τ are the product pricing process, and ωr, ωπ, ωy and ωμ are the process of monetary policy. Then, 7 shocks are defined with 14 parameters. The initial distributions are given in Table 3.Table 3
The definitions and initial distributions of the dynamic parameters.
Dynamic parametersInitial distributionsParameterDefinitionDistributionPrior meanStandard variancePosterior meanσcReciprocal of intertemporal consumption elasticity of substitutionNormal10.2631.374kNonfruit consumption rateNormal0.80.10.743ψInvestment adjustment coefficientNormal3.514.0ξpPrice adjustment probabilityBeta0.50.10.79ξwWage adjustment probabilityBeta0.50.10.81τSteady-state inflation weightBeta0.50.10.47ωrCentral bank reaction coefficientBeta0.50.10.25ωπGamma2.511.07ωyGamma2.512.83ωμGamma1.50.52.77θaConsumption preference shockBeta0.50.10.703θxInvestment adjustment shockBeta0.50.10.552θtwWage plus shockBeta0.50.10.676γtpPrice plus shockBeta0.50.10.600δzTechnology shockBeta0.50.10.582δpfFruit price shockBeta0.50.10.537ρvMonetary policy shockBeta0.50.10.662σa2Consumption preference shockInv.gamma0.1100.127σx2Investment adjustment shockInv.gamma0.10.0020.179σγw2Wage plus shockInv.gamma0.10.0020.194σγp2Price plus shockInv.gamma0.10.0020.180σz2Technology shockInv.gamma0.10.0020.203δpf2Fruit price shockInv.gamma0.10.0020.382σv2Monetary policy shockInv.gamma0.10.0020.443According to the Bayesian estimates, the intertemporal consumption elasticity of substitution1/σ_c is 0.728, which means that the interest rate has a large effect on the household consumption level. When the interest rate rises, people will save more and consume less. Non-fruit consumption rate k is 0.743, and fruit consumption rate 1 − k is 0.257, which means that, in Hainan, fruit consumption takes up a large proportion of total consumption. The value of investment adjustment cost ψ is 4, which means that, in China, it takes a long time for an investment plan to operate.The value of price adjustment probabilityξp is 0.79, which means that, in China, the goods price is extremely sticky. This means that, every year, 21% of companies can adjust their price, while 79% of companies cannot adjust their price and remain profitable. The value of wage adjustment probability ξw is 0.81, which means that, in China, 19% of people can adjust their wage. The value of τ is 0.47.For the central bank reaction coefficient, the value ofωy is 2.83, and the value of ωπ is 1.07, which means that, in China, monetary policy is correlated with output. The value of ωr is 0.25, and the value of ωμ is 2.77, which means that the impact of interest rates is smaller than the impact of money supply. This is consistent with the observed Chinese situation, where money supply plays a large role in the economy.For the shock descriptive parameters,θx, θtw, δz, δpf and ρv, θa, γtp are all greater than 0.5, which means that, for consumption preference shock, price shock, fruit price shock, and monetary policy shock, they are all coherent. For the shock relative fluctuation, σa2, σx2, δpf2 and σv2, σγw2, σγp2, and σz2 are all greater than 0.1, which means that the violation of these four variables is greater.


### 4.3. Impulse Analysis

According to the calibration and the parameter values of Bayesian estimation, which are mentioned above, the impulse response diagram of a single fruit price shock to 11 macroeconomic variables such as output, consumption, investment, inflation, labor demand, real money balances, nominal interest rates, value of capital investment, real wages, fruit products consumption, and fruit raw materials input were simulated to analyze the different effects of fruit price shock on macroeconomic fluctuations. It is worth noting that the impulse response diagram of this model is not the actual values of these 11 variables, but the deviations from steady-state values.As shown in Figure2, the rapid increase in the price of fruit would have a significant negative impact on Hainan’s economy. When the price of fruit rises by 1%, the total output of Hainan Province will fall by 0.04%, as shown in Figure 2(a). The rising prices of the fruit will lead to higher production costs and reduced output in the related industry. However, the fruit industry is the pillar industry of Hainan province, and with the fruit price rising, the output of fruit industry will be reduced correspondingly, and then the GDP of Hainan will be influenced. At the same time, the fruit price shock also impacts the inflation of Hainan province. When the price of fruit rises by 1%, the CPI will fall by 0.2%, as shown in Figure 2(b). The production costs will be increased with the rising prices of fruit, and it will result in the cost-push inflation.Figure 2
The effect of fruit price increases on output and CPI.
(a)(b)The results shown in Figure3 are consistent with the Chinese economy: there is higher GDP growth and higher inflation at the same time. Accordingly, the money supply increases by 0.09% and then decreases, which is consistent with Chinese monetary policy, as shown in Figure 3(a). The investment will go up by 0.03 due to the rapid increase in the price of fruit, as shown in Figure 3(b). This is easy to understand, as higher price will attract people to do the investment. The consumption of fruit decreases by 0.05% when the price of fruit is increasing, as shown in Figure 3(c). This is consistent with the fact that when the price of a good increases, the demand will decrease. Also, when the price of fruit is increasing, the consumption of non-fruit increases by 0.015%, as shown in Figure 3(d). This is also consistent with economics principle. When one good’s price is increasing, people will choose to consume other goods, which have lower price. The fruit production input decreases by 0.01%, as shown in Figure 3(e). This is due to the fact that higher price means higher cost. Thus, rational people will choose to input less. Finally, the labor will increase, as shown in Figure 3(f), and wages will increase due to inflation and then decrease, as shown in Figure 3(g).Figure 3
The impulse reaction of variables related to the price of fruit.
(a)(b)(c)(d)(e)(f)(g)


### 4.4. Variance Decomposition

We also perform the variance decomposition, which shows the results in Table4.Table 4
The variance decomposition of variables.
TimeYCon.Invest.MoneyCPIWageFruit output1100000000542.7620.27326.35117.4560.48611.8640.8081030.4677.48340.53513.6961.6585.5730.5881524.5689.47430.35724.9564.2835.7280.6342020.5468.46134.97223.5977.4134.3880.6232517.5328.03437.72324.9746.0234.9800.7343016.7537.97536.67123.5928.5425.8720.5953515.5768.59737.83822.9578.7825.4730.7774014.5249.79436.29123.2149.2625.6410.874In the short time, the impulse of output comes from itself, which is 42.762%. As time passes, the impulse of output is 14.524%. Meanwhile, the investment has the highest influence on output, which increases from 26.351% to 36.291%. This implies that investment has the most important influence on economic development, which is consistent with the observed situation in Hainan. The monetary influence is the second most important, which accounts for 23.214% over the longest time period. This implies that monetary policy has a large effect on the economy. Consumption and CPI have a small effect on output, which implies that these two variables have a lag effect on output. The effect of wages decreases over time, and the effect of fruit output changes an extremely small amount.


## 4.1. Data

The data used in this paper is the total output, investment, money supply, wages, inflation, and the percentage change of fruit consumption from state values. The data is from 2004 to 2017. We use GDP and The Total Sales of Consumer Goods as total output in Hainan, Total Investment in Fixed Assets as investment, M2 in Hainan as money supply, and the Total Output of Fruit Production as fruit consumption. The inflation is calculated using CPI in 2004 as the base element.


## 4.2. Parameter Estimation

The parameters in this paper are calculated using two methods. For some fixed parameters, the values are taken from the literature related the Chinese economy. For dynamic parameters, we estimate them using a Bayesian method.The total number of parameters in this paper is 11:β, σL, ζ, δ, ∂1, ∂2, ∂3, σM, εc, εi, εf.β is the discount factor. In China, the interest rate for a one-year deposit is 2.75%; therefore, we get the value of β as 0.973. σL is the rate of labor negative utility. When we assume that the labor supply market is a monopoly competitive market, the value of σL is between 0.3 and 1 [18]. Based on the study by CMR (2007), we set the value of σL to be equal to 1. σM is the rate of monetary utility, based on Tong [24], and we choose 1.4 as the value of σM.δis the capital depreciation rate, which is equal to 10% for one year in this paper as the previous research [19]. ζ represents the monopoly level of the market. ζ can be calculated by the steady-state price addition of θω. Based on Ireland [4], we choose 6 as the value of θω, and then the value of ζ is 1.2, which means that the steady state price plus is 20%.∂1, ∂2 and ∂3 represent the ratio of input during the process of intermediate goods production. Based on Tong [24] calculated the actual data of China by the income approach and developed the value of ∂1 to be 0.6, which means that the labor income accounts for 60% of the total income of intermediate products in the steady state. According to Ireland [4], the assumed value of ∂2is 0.21. Because ∂1 + ∂2 + ∂3 = 1, the calculated value of ∂3 is 0.19.According to the calculation,εc, εi and εf represent the ratio of non-fruit consumption, investment, and fruit consumption to GDP, which are 0.372, 0.528, and 0.1, respectively. Table 2 shows the definitions and the values of fixed parameter.Table 2
Fixed parameter definitions and their values.
ParameterDefinitionValueβDiscount factor0.973σLThe rate of labor negative utility1ζMonopoly level of market1.2δCapital depreciation rate0.01∂1Labor elasticity0.6∂2Capital elasticity0.21∂3Fruit elasticity0.19σMThe rate of monetary utility1.4εcNonfruit consumption to GDP0.372εiInvestment to GDP0.528εfFruit consumption to GDP0.1The number of dynamic parameters in this paper is 24.σc and k are the economic behaviors of representative household, ψ is the investment behaviours, ξw is the wage pricing process, ξp and τ are the product pricing process, and ωr, ωπ, ωy and ωμ are the process of monetary policy. Then, 7 shocks are defined with 14 parameters. The initial distributions are given in Table 3.Table 3
The definitions and initial distributions of the dynamic parameters.
Dynamic parametersInitial distributionsParameterDefinitionDistributionPrior meanStandard variancePosterior meanσcReciprocal of intertemporal consumption elasticity of substitutionNormal10.2631.374kNonfruit consumption rateNormal0.80.10.743ψInvestment adjustment coefficientNormal3.514.0ξpPrice adjustment probabilityBeta0.50.10.79ξwWage adjustment probabilityBeta0.50.10.81τSteady-state inflation weightBeta0.50.10.47ωrCentral bank reaction coefficientBeta0.50.10.25ωπGamma2.511.07ωyGamma2.512.83ωμGamma1.50.52.77θaConsumption preference shockBeta0.50.10.703θxInvestment adjustment shockBeta0.50.10.552θtwWage plus shockBeta0.50.10.676γtpPrice plus shockBeta0.50.10.600δzTechnology shockBeta0.50.10.582δpfFruit price shockBeta0.50.10.537ρvMonetary policy shockBeta0.50.10.662σa2Consumption preference shockInv.gamma0.1100.127σx2Investment adjustment shockInv.gamma0.10.0020.179σγw2Wage plus shockInv.gamma0.10.0020.194σγp2Price plus shockInv.gamma0.10.0020.180σz2Technology shockInv.gamma0.10.0020.203δpf2Fruit price shockInv.gamma0.10.0020.382σv2Monetary policy shockInv.gamma0.10.0020.443According to the Bayesian estimates, the intertemporal consumption elasticity of substitution1/σ_c is 0.728, which means that the interest rate has a large effect on the household consumption level. When the interest rate rises, people will save more and consume less. Non-fruit consumption rate k is 0.743, and fruit consumption rate 1 − k is 0.257, which means that, in Hainan, fruit consumption takes up a large proportion of total consumption. The value of investment adjustment cost ψ is 4, which means that, in China, it takes a long time for an investment plan to operate.The value of price adjustment probabilityξp is 0.79, which means that, in China, the goods price is extremely sticky. This means that, every year, 21% of companies can adjust their price, while 79% of companies cannot adjust their price and remain profitable. The value of wage adjustment probability ξw is 0.81, which means that, in China, 19% of people can adjust their wage. The value of τ is 0.47.For the central bank reaction coefficient, the value ofωy is 2.83, and the value of ωπ is 1.07, which means that, in China, monetary policy is correlated with output. The value of ωr is 0.25, and the value of ωμ is 2.77, which means that the impact of interest rates is smaller than the impact of money supply. This is consistent with the observed Chinese situation, where money supply plays a large role in the economy.For the shock descriptive parameters,θx, θtw, δz, δpf and ρv, θa, γtp are all greater than 0.5, which means that, for consumption preference shock, price shock, fruit price shock, and monetary policy shock, they are all coherent. For the shock relative fluctuation, σa2, σx2, δpf2 and σv2, σγw2, σγp2, and σz2 are all greater than 0.1, which means that the violation of these four variables is greater.


## 4.3. Impulse Analysis

According to the calibration and the parameter values of Bayesian estimation, which are mentioned above, the impulse response diagram of a single fruit price shock to 11 macroeconomic variables such as output, consumption, investment, inflation, labor demand, real money balances, nominal interest rates, value of capital investment, real wages, fruit products consumption, and fruit raw materials input were simulated to analyze the different effects of fruit price shock on macroeconomic fluctuations. It is worth noting that the impulse response diagram of this model is not the actual values of these 11 variables, but the deviations from steady-state values.As shown in Figure2, the rapid increase in the price of fruit would have a significant negative impact on Hainan’s economy. When the price of fruit rises by 1%, the total output of Hainan Province will fall by 0.04%, as shown in Figure 2(a). The rising prices of the fruit will lead to higher production costs and reduced output in the related industry. However, the fruit industry is the pillar industry of Hainan province, and with the fruit price rising, the output of fruit industry will be reduced correspondingly, and then the GDP of Hainan will be influenced. At the same time, the fruit price shock also impacts the inflation of Hainan province. When the price of fruit rises by 1%, the CPI will fall by 0.2%, as shown in Figure 2(b). The production costs will be increased with the rising prices of fruit, and it will result in the cost-push inflation.Figure 2
The effect of fruit price increases on output and CPI.
(a)(b)The results shown in Figure3 are consistent with the Chinese economy: there is higher GDP growth and higher inflation at the same time. Accordingly, the money supply increases by 0.09% and then decreases, which is consistent with Chinese monetary policy, as shown in Figure 3(a). The investment will go up by 0.03 due to the rapid increase in the price of fruit, as shown in Figure 3(b). This is easy to understand, as higher price will attract people to do the investment. The consumption of fruit decreases by 0.05% when the price of fruit is increasing, as shown in Figure 3(c). This is consistent with the fact that when the price of a good increases, the demand will decrease. Also, when the price of fruit is increasing, the consumption of non-fruit increases by 0.015%, as shown in Figure 3(d). This is also consistent with economics principle. When one good’s price is increasing, people will choose to consume other goods, which have lower price. The fruit production input decreases by 0.01%, as shown in Figure 3(e). This is due to the fact that higher price means higher cost. Thus, rational people will choose to input less. Finally, the labor will increase, as shown in Figure 3(f), and wages will increase due to inflation and then decrease, as shown in Figure 3(g).Figure 3
The impulse reaction of variables related to the price of fruit.
(a)(b)(c)(d)(e)(f)(g)


## 4.4. Variance Decomposition

We also perform the variance decomposition, which shows the results in Table4.Table 4
The variance decomposition of variables.
TimeYCon.Invest.MoneyCPIWageFruit output1100000000542.7620.27326.35117.4560.48611.8640.8081030.4677.48340.53513.6961.6585.5730.5881524.5689.47430.35724.9564.2835.7280.6342020.5468.46134.97223.5977.4134.3880.6232517.5328.03437.72324.9746.0234.9800.7343016.7537.97536.67123.5928.5425.8720.5953515.5768.59737.83822.9578.7825.4730.7774014.5249.79436.29123.2149.2625.6410.874In the short time, the impulse of output comes from itself, which is 42.762%. As time passes, the impulse of output is 14.524%. Meanwhile, the investment has the highest influence on output, which increases from 26.351% to 36.291%. This implies that investment has the most important influence on economic development, which is consistent with the observed situation in Hainan. The monetary influence is the second most important, which accounts for 23.214% over the longest time period. This implies that monetary policy has a large effect on the economy. Consumption and CPI have a small effect on output, which implies that these two variables have a lag effect on output. The effect of wages decreases over time, and the effect of fruit output changes an extremely small amount.


## 5. Conclusions and Further Research

Based on the perspective of sustainable development, this study explores the effective way to solve the competition of tropical fruits industry between China and Southeast Asia. Based on the demand side of the structure of the adjustment and the macroeconomics perspective, we build a small-scale, regionalization, and specialized DESG model using Chinese annual data from 2004 to 2017 estimated by the maximum likelihood method to analyze the fluctuation of fruit prices on the economy. We find that increasing price has a negative effect on fruit output. When this happens, it is preferable to loosen monetary policy to reduce this influence. The reason is that loosening monetary policy will result in price inflation, which will lead to a decreasing output simultaneously.In reality, it is difficult to find a case where monetary policy is changed due to price fluctuations of a certain product. Because the monetary and finance systems are extremely complicated nonlinear systems and contain many complex factors [25], we should try to maintain the relative stability of the monetary and finance system. For the quick and healthy development of the economy, it is not too active to be chaotic, which is difficult to forecast and control, nor too faded to lose the energy [25]. From policymaker perspective, government intervention policies can maximize the social welfare [26], but chaos occurs with the increase in the farmer’s sensitivity. If government regulates within a reasonable range, the chaos can be controlled, and the system’s profits rise [27]. Therefore, we put forward some suggestions to promote the sustainable development of fruit industry in Hainan.Firstly, based on the impact of the fruit price on economy, supply-side structural adjustment should be adopted. We recommend adjusting the supply structure of the fruit industry by developing a sharing economy business system [28] as shared-farms model and gradually integrating the primary, secondary, and tertiary industries, and it will contribute to the sustainable economic system.Secondly, the rising costs of labor led to the gradual loss of price advantage, and the contribution of competitiveness to the growth of Hainan’s fruit exports has rapidly declined [29]. The government should focus on the selection of fruit varieties, optimization of the industrial structure, and supporting policies. The structure of the fruit industry should be adjusted, and a competitive market should be developed with high quality fruit varieties as organic fresh fruits [30]. Planning should be done based on the characteristics of different locations to efficiently build a large base of fruit varieties, while strengthening management and increasing investment or subsidy in science and technology. But attention should be paid to the strategy of subsidies, because subsidy may always have negative impact on the system’s stability, which may drive the system operation to be uncontrollable [31].Thirdly, the investment in the fruit industry should be increased. Banks should provide loans for firms to invest according to the characteristic of economy [32]. It can be seen from our analysis that the investment has a significant stimulating effect on fruit output. Also, the fruit industry chain should be extended by increasing the construction of fruit industry facilities or developing the e-commerce, which will help decrease the natural, technological, and market risks. If the retailer, holding symmetric channel power with the farmer, will increase its profit, in an asymmetric channel power supply chain, the whole profit of supply chain will be lower than the one in a symmetric channel power supply chain [33]. So, developing e-commerce is one of the best ways to hold symmetric channel power and increase its profit.Fourthly, a multi-fruit industry sustainable system should be established. The prevalence of opportunistic behaviors in agrifood production and circulation results in frequent quality accidents in emerging economies. The quality information tracing technology, farmers, and marketers’ fair distribution of profits and risks, and consumers’ capabilities to safeguard their legal rights are the three key factors to maintain the effectiveness and stability of quality assurance systems [34]. We should establish a multi-fruit industry sustainable system from the above three aspects. These include the establishment and improvement of early warning systems for damage to the fruit industry and rapid response mechanisms.There are some different contributions of this study. From the theoretical perspective, we advance the dynamic stochastic general equilibrium model with a new specialized DSGE model, which consists of the representative household, finished goods-producing company, intermediate goods producing company, and central bank. This has not been previously investigated in the macroeconomic literature. In addition, we develop a typology including six different shocks, as well as actual fruit price fluctuation, thus highlighting the importance of studying a sustainable economic system, which includes the fruit industry. On the other hand, from a managerial perspective, through our study, we reveal the link between the fluctuation of increasing fruit prices and fruit output. Also, we make suggestions focusing on the fruit industry sustainable growth for the Hainan economy on some policy aspects.Though the paper, we explain the phenomena extremely well, and there is scope for further research. This paper uses sticky prices of Calvo [20] to build a small-region DSGE model to explain the effect of fruit prices in Hainan. For the complete DSGE model, we did not consider the effect of monetary policy. Correct monetary policy can effectively help the economy withstand external impacts. The question of whether monetary policy is the main cause of an economic recession after a fruit shock can serve as the focus of future research. By modifying the rules function and adjusting the choice of monetary policy, combined with a small-region DSGE model constructed in this paper, we could, respectively, discuss the performance of the entire economy under the circumstances, where monetary authorities must deal with the inflation gap, the output gap, and no gap. It would serve as a basis to find suitable monetary policy for Hainan to deal with the impact of fruit prices.



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*Source: 6693709-2021-06-16.xml*