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Motivated by the facts that the sharp volatility in international oil prices has become one of the important external sources in driving China’s economic fluctuations, and in view of the strong correlation between oil and consumer durables, we build a real business cycle (RBC) model incorporating durable goods consumption in the context of oil price shocks. Using quarterly data on Chinese economy to conduct an empirical test, we examine China’s cycle characteristics of macroeconomic volatility and the transmission mechanism of oil price shocks. The study shows: 1) In the RBC model the consumption will be divided into durables and non-durables, which plays a crucial role in explaining Chinese economic fluctuations. The core of the model is to improve the forecast of consumption volatility and weak pro-cyclicality, which is closer to the actual economy; 2) Oil price shocks mainly affect consumption volatility, but seldom influence output, investment and labor, the three variables of which are largely influenced by technology shocks; 3) The model reveals that the transmission mechanism is determined by intra-temporal income effects and inter-temporal effects of portfolio rebalanced between durable goods and capital goods.

Since its reform started in 1978, China’s economy has sustained high growth about 8% - 10%^{1}, shoring up the demand for oil. As early as 2003, China has surpassed Japan to become the world’s second largest oil consumer after the United States. With a sharp rise in the consumption scale, external dependence of crude oil is also rising. Since the year 2011, China has surpassed the US as the world’s largest oil importer; in 2012, China’s net oil imports accounted for 86% of the global growth increment; its dependence on foreign oil in 2014 reached 59.5% of its overall consumption. From the beginning of this century, international oil prices have gone up and down for more than 50% for three times. Take the recent market for example, since the second half of 2014, the British Brent crude oil prices fell more than 60% in less than seven months, second only to the financial crisis in 2008. The sharp volatility in international oil prices has become one of the important external sources in driving business cycle fluctuations in China. As a major energy and raw material in modern industry, oil price volatility influences a nation’s macro-economy through a variety of channels [

It should be emphasized that, in recent years, the driving forces for China’s oil consumption growth not only come from industrialization and urbanization, but also from changes in the structure of consumer demand. The consumption structure of Chinese residents has gone from subsistence to well-off, and then upgraded to be the consumer. On one hand, the proportion of total food consumption is on decline, with the Engel coefficient of urban residents decreasing from 57.5% in 1978 to 35.0% in 2013, and rural residents from 67.7% to 37.7% (from China Statistical Yearbook, 2014). On the other hand, the types of consumer goods continue to be enriched and the quality continues to be improved, among which the most obvious sign is that the various durable goods of residents have continued to be on increase. Not only has the amount of color television sets, refrigerators and other traditional home appliances are on fast rise^{2}, other newly developing household consumptions such as personal computers, mobile phones, sports cars and other entertainment equipment are significantly expanded^{3}. Oil as a raw material is widely involved in the production of consumer durables sectors, but also used as input and fuel in durable goods. The consumption upgrading has led to the transformation of the industrial structure, and boosted the demand for oil.

Distinctive from consumer non-durable goods (non-durables) consumption, durable goods (durables) have higher prices and long-term use for each time. In addition, durables consumption behavior is obviously different from other consumer behaviors. On one hand, to those durables that do not belong to the necessities of life, households can selectively consume according to income in different periods, so the intertemporal elasticity of substitution is much bigger than that of non-durables [

Firstly, with regard to oil price shocks, there are a series of influential works in the field of oil price shocks based on RBC framework [

Secondly, as to durables consumption, mainstream literatures can be divided into durables and non-durables and its impact of macro-economy. Durables refer to the automobiles, household goods, sports equipment, jewelry and other goods that don’t quickly wear out, while non-durables are the opposite of durables, such as a short or one-time consumption of goods and services. The motivation for scholars to make such a distinction lies in that in one way, different pace of expenditure and intertemporal elasticity of substitution between two kinds of goods will affect the growth speed of the actual economy; in another way, durables are much sensitive to the economic policy, particularly the monetary policy, than the non-durables, which will lead to changes in policy transmission mechanism and optimal economic policy. Studies are represented by Ogaki and Reinhart (1998), Erceg and Levin (2006), and Monacelli (2009) [

Throughout these studies, it can be found that for Chinese economy, discussion of the oil price volatility and durables consumption are separated in the study of economic relations, either simply on the oil price impact on the economy, or just on the role of durables in the economy. There is little literature discussing the complementary nature of them. Moreover, those studies exploring the macroeconomic effects through dividing the consumer goods into durables and non-durables are focused on quantitative analysis, whereas the study of the impact of consumer durables in RBC framework is not yet involved. Meanwhile, if missing the reality features described by the rising durables consumption of urban and rural residents in China, such modelling may bring forth error of fitting and it is difficult to accurately capture the oil price impact on China’s macroeconomic mechanisms. In addition, when establishing the RBC theoretical framework of oil economy, the existing literature is silent on using actual economic data to test whether the model really applies to China’s cyclical properties.

In view of this, based on RBC framework, our work complements these studies by incorporating non-durables and durables to investigate the transmission mechanism of oil prices on the economy, and moreover shows the patterns of China’s business cycle in the context of oil price shocks. Compared with the most existing studies, the contribution of the paper is three-fold: first, we conduct an RBC exercise using quarterly data rather than annual data through the abundant studies in RBC models talking about China’s business cycle [

The remainder of this paper is organized as follows. Section 2 describes cyclical properties of oil price and other macro series in China; Section 3 presents the RBC model of oil economy, including durables and non-durables consumption. Section 4 conducts on calibration for parameters. Section 5 discusses model results. Section 6 concludes the paper.

This paper uses data from the databases of CICE and WIND, with the choice of quarterly data and a time span from 1997Q1 (1997Q1 means the first quarter of 1997, the same below) to 2016Q1, a total of 77. China has officially compiled quarterly data since the 1990s, while from 1997 the National Bureau of Statistics of China (NBS) began to announce monthly or quarterly consumer durables data, goods such as the car/furniture/appliances/sports and entertainment products. Durables data are crucial to the modeling and analysis of our work so the sample is selected from the beginning of 1997. In order to be consistent with the results of the DSGE theory below, seasonal adjustment of variables is made except oil prices and labor, and then all variables are in logarithms and have been de-trended with the HP filter.

According to CPI on a yearly basis and monthly series published by NBS, quarterly fixed base ratio based on 1997Q1 can be figured out, and quarterly GDP deflator is used to calculate the actual value of the relevant economic variables.

Firstly, the actual consumption is the outcome of the total quarterly retail sales of consumer goods divided by quarterly GDP deflator.

Secondly, unlike the US, Chinese consumption official statistics have not been carried out for durables and non-durables. With reference to the mainstream literature classification method and the availability of China data, four representative variables of durables, namely, the car/furniture/appliances/sports and entertainment products, can be divided by quarterly GDP deflator, and then comes out the actual durables investment.

Thirdly, since there is no quarterly or monthly private investment data in the statistics officially published, which is consistent with Wang and Zhu (2015), the domestic loans, self-financing, foreign investment, and other capitals will be taken as representative variables of the total funds for private investment [

Fourthly, the actual total investment is defined as the investment total of actual private investment and durables investment.

Fifthly, using “unit employees in total” as labor is applied in Huang (2005).

Sixthly, the actual GDP is nominal GDP divided by the quarterly GDP deflator.

Seventhly, “retail: enterprises over the quota: petroleum and petroleum products” can be obtained as representative variables for household oil consumption. If this series is further divided by the quarterly GDP deflator, the actual household oil consumption will be obtained.

Eighthly, the use of the West Texas Intermediate (WTI) crude oil spot prices^{4} in which the monthly data using the geometric mean method become quarterly data, then converted to RMB price, and divided by quarterly GDP deflator to obtain actual oil prices.

From

First, oil prices and household oil consumption are more volatile than capital investment, durables investment, and GDP, and volatilities of labor and consumption

GDP | Consumption | Capital investment | Durables investment | Total investment | Household oil consumption | Labor | Oil price | |
---|---|---|---|---|---|---|---|---|

Standard deviation | 0.0376 | 0.0174 | 0.0593 | 0.0528 | 0.0519 | 0.0796 | 0.0245 | 0.2073 |

Relative standard deviation | 1.00 | 0.46 | 1.57 | 1.40 | 1.38 | 2.12 | 0.65 | 5.51 |

Autocorrelations | 0.48 | 0.71 | 0.50 | 0.59 | 0.61 | 0.75 | 0.49 | 0.69 |

Contemporaneous correlations with GDP | 1 | 0.15 | 0.74 | 0.52 | 0.88 | 0.04 | 0.78 | 0.06 |

Note: See the first paragraph in this section of the data sources and data processing described; relative standard deviation is the ratio of standard deviation of the variables to standard deviation of the GDP; autocorrelations refer to the first-order autocorrelation coefficient.

are the lowest. On one hand, capital investment and durables investment are more severe volatilities, 1.58 times and 1.40 times of the amplitude of GDP respectively, also showing a strong pro-cyclicality. On the other hand, volatility in labor is smoother, proving that China’s features are different from business cycles in the developed markets as well as other emerging markets.

Second, one striking fact is that consumption is slightly pro-cyclical with a correlation of only 0.15, as opposed to China’s strong pro-cyclicality derived from annual data produced by Rao and Liu (2014), as well as different from strong pro-cyclicality of the US data [

Third, the autocorrelations of consumption and durables investment are 0.71 and 0.59 respectively, indicating strong “consumer” inertia in both of them, which is in line with “Catch up with the Joneses” [

Four, volatility in oil prices is as high as 0.2073, three times greater than capital investment, which shows the volatility of oil prices may be an important source of external shocks for China’s economic fluctuations. Meanwhile, the low correlation (0.06) between oil prices and GDP may also indicate the asymmetry, the alternative and the complexity between oil prices and the economy, requiring comprehensive and dynamic researches on the inherent association between oil prices and China’s macroeconomics, among which DSGE model is just able to provide an analytical framework that combines short and long term, overt and unity.

Based on the canonical RBC model framework developed by Hansen (1985) and Cooley and Prescott (1995), this paper refers to the setting mode of Dhawan and Jeske (2007) model, thus set the production function into the form of “capital-oil-labor”, which is a three elements double nested structure. The consumer goods of household sector are also divided into durables and non-durables in the utility function to build a DSGE model of oil economy containing both households and firms.

The representative household consumption ( C t ) consists of durables ( D t ), oil and oil-products ( O h , t , hereinafter referred to oil) and non-durables ( N t ). Assume the double nested CES functional form is constituted by three elements:

C t = [ α c ( N t ) − ρ c + ( 1 − α c ) ( F t ) − ρ c ] − 1 ρ c (1)

F t ≡ [ α F ( D t − 1 ) − ρ F + ( 1 − α F ) ( O h , t ) − ρ F ] − 1 ρ F (2)

α c ∈ ( 0 , 1 ) , α F ∈ ( 0 , 1 ) , ρ c ≥ − 1 , and ρ F ≥ − 1 , where 1 1 + ρ c is the elasticity of substitution between the composite of oil and durables (defined as F t ) and non-durables, and 1 1 + ρ F is the elasticity of substitution between oil and

durables. There is an accumulative process of consumption for durables and the operating mode is similar to the capital ( K t ) in the model, both belonging to the state variables.

The representative household utility function is as follows:

E 0 { ∑ t = 0 ∞ β t [ log ( C t ) − ( L t ) 1 + η 1 + η ] } (3)

where β denotes the discount factor， L t is the labor supply variable， η is the inverse of the elasticity of labor supply. The budget constraint for households is:

N t + I K , t + I D , t + P o , t O h , t = w t L t + r t k K t − 1 (4)

I K , t and I D , t are the investments of capital and durables respectively. w t and r t k denote real wages and return on invested capital. P o , t is the actual price of oil. In addition, the stock of given capital and durables evolves according to:

I K , t = K t − ( 1 − δ k ) K t − 1 + ∅ k 2 ( I K , t K t − 1 − δ k ) 2 K t − 1 (5)

I D , t = D t − ( 1 − δ d ) D t − 1 + ∅ d 2 ( I D , t D t − 1 − δ d ) 2 D t − 1 (6)

δ k and δ d are discount factors of capital and durables respectively. In line with the setting mode of Atkeson and Kehoe (1999), it is assumed that the investments of capital and durables bring about additional adjustment costs, so ∅ k and ∅ d are defined as the parameters for adjustment costs [

The first order condition is obtained by solving the dynamic optimal choice problem of the representative household:

λ t = α c ( C t ) ρ c ( N t ) − 1 − ρ c (7)

λ t Q D , t = β { ( 1 − α c ) α F ( C t + 1 ) 1 + ρ c ( F t + 1 ) ρ F − ρ c ( D t ) − ( 1 + ρ F ) + λ t + 1 Q D , t + 1 [ ( 1 − δ d ) − ∅ d 2 ( I D , t + 1 D t − δ d ) 2 + ∅ d I D , t + 1 D t ( I D , t + 1 D t − δ d ) ] } (8)

λ t P o , t = ( 1 − α c ) ( 1 − α F ) ( C t ) ρ c ( F t ) ρ R − ρ c ( O h , t ) − 1 − ρ F (9)

λ t w t = ( L t ) η (10)

Q K , t = β λ t + 1 λ t { r t k + Q K , t + 1 [ ( 1 − δ k ) − ∅ k 2 ( I K , t + 1 K t − δ k ) 2 + ∅ k I K , t + 1 K t ( I K , t + 1 K t − δ k ) ] } (11)

Q K , t [ 1 − ∅ k ( I K , t K t − 1 − δ k ) ] = 1 (12)

Q D , t [ 1 − ∅ d ( I D , t D t − 1 − δ d ) ] = 1 (13)

where λ t is the Lagrange multiplier of budget constraint, Q K , t and Q D , t are the shadow prices (i.e. the Lagrange multipliers of capital and durables accumulation equations) of capital and durables, respectively. (7), (8) and (9) are Euler equations of non-durables, durables and household oil consumption, which describe the optimal consumption choices of the household on these three goods. (10) is the supply equation of labor and (11) is the Euler equation of capital. (12) and (13) characterize the optimal dynamic investment behaviors of capital and durables.

Same with the settings of household sector, the production function of firms is a double nested CES^{5} functional form constituted by three elements:

Y t = A t [ α y ( X t ) − ρ y + ( 1 − α y ) ( L t ) − ρ y ] − 1 ρ y (14)

X t ≡ [ α x ( K t − 1 ) − ρ x + ( 1 − α x ) ( O f , t ) − ρ x ] − 1 ρ x (15)

Y t is the production, O f , t is the oil consumption of firms, X t is the composite of capital and oil ( similar to F t in household sector), A t is neutral technology shock, also known as the so-called total factor productivity (TFP) and its logarithmic form follows the stochastic process below:

ln ( A t ) = ( 1 − ρ A ) ln ( A ) + ρ A ln ( A t − 1 ) + u A , t , u A , t ~ N ( 0 , ( σ A ) 2 )

where ρ A ∈ ( 0 , 1 ) is the autoregressive coefficient, A is its steady state value, σ A is the standard deviation of technology shocks. Also, α y ∈ ( 0 , 1 ) , α x ∈ ( 0 , 1 ) , ρ y ≥ − 1 , ρ x ≥ − 1 .

We can derive the first order condition with respect to L t , K t and O f , t by solving the profit maximization problem of firms:

w t = ( 1 − α y ) ( A t ) − ρ y ( Y t / L t ) 1 + ρ y (16)

r t k = α y α x ( A t ) − ρ y ( X t ) ρ x − ρ y ( Y t ) 1 + ρ y ( K t − 1 ) − ( 1 + ρ x ) (17)

P o , t = α y ( 1 − α x ) ( A t ) − ρ y ( X t ) ρ x − ρ y ( Y t ) 1 + ρ y ( O f , t ) − ( 1 + ρ x ) (18)

So far, we have characterized the optimal choices of the households and firms under constraints: the maximization of expected utility of households and the maximization of expected profits of firms, so the market clearing of the final good is:

N t + I K , t + I D , t + P o , t ( O h , t + O f , t ) ≤ Y t (19)

In recent years, oil coming from abroad has accounted for an increasing proportion of China’s aggregate amount. Chinese external dependence of petroleum and crude oil both broke the point of 55% in 2011, surpassed the US as the highest in the world. Thus the oil price volatility is highly relevant with the international market of crude oil. In addition, China has started late on transactions of staple commodities, which results in some problems about the market like the few varieties, small size, low openness and the lack of pricing power. So the oil pricing in China depends on the international market to some extent. In order to focus on analyzing the impact of oil price on China’s macro-economy, consistent with the assumptions of Rotemberg and Woodford (1996) on US crude oil, we assume that volatility of oil prices in China depends on the international market, that is to say the oil price is completely exogenous and follows the ARMA (1, 1) process (see the parameter calibration part in the next chapter). The final log-linearization is:

P ^ o , t = ρ o P ^ o , t − 1 + u ^ o , t + ρ u u ^ o , t − 1 , u o , t ~ N ( 0 , ( σ o ) 2 )

ρ o and ρ u are the coefficients of the oil price ARMA (1, 1) respectively, σ o is the standard deviation of actual oil price shocks. At the same time, a part of the output components should be used to pay for the imported oil, so the relation is: V A t = Y t − P o , t ( O h , t + O f , t ) . The difference value is defined as the value added of production ( V A t ), combined with the market clearing equation of final good:

V A t = N t + I K , t + I D , t (20)

Finally, by solving the log-linearized equations, optimal equilibrium path for each endogenous variable can be obtained:

{ C t , N t , D t , O h , t , F t , I D , t , I K , t , w t , L t , r t k , K t , Y t , X , O f , t , λ t , Q D , t , Q K , t , V A t }

The purpose of this paper is to examine the relevance of oil prices and China’s economy, thus how to determine the correlation coefficient of oil price shocks is particularly important. Through trial and error, it is found that ARMA (1, 1) model can fit the actual fluctuating trend of oil prices in the sample period, as seen in

Based on quarterly frequency data, Wang et al. (forthcoming) find the first-order regression coefficient of China’s technology shock is 0.8, which is slightly lower

Sample (adjusted): 1997Q2 2016Q1 Included observations: 76 after adjustments Convergence achieved after 10 iterations MA Backcast: 1997Q1 Sample (adjusted): 1997Q2 2016Q1 | ||||
---|---|---|---|---|

Variable | Coefficient | Std. Error | t-Statistic | Prob. |

AR (1) | 0.555378 | 0.122424 | 4.536497 | 0.0000 |

MA (1) | 0.456640 | 0.134248 | 3.401468 | 0.0011 |

R-squared | 0.579268 | Mean dependent var | −0.003815 | |

Adjusted R-squared | 0.573582 | S.D. dependent var | 0.205956 | |

S.E. of regression | 0.134491 | Akaike info criterion | −1.148676 | |

Sum squared resid | 1.338498 | Schwarz criterion | −1.087341 | |

Log likelihood | 45.64970 | Hannan-Quinn criter. | −1.124164 | |

Durbin-Watson stat | 1.894332 |

than 0.95 of the US [

1) The discount factor β

From 1997Q1-2016Q1, the average inflation growth rate on a quarter-to-quarter basis is 1%, so the quarterly discount factor is set at 0.99.

2) Capital depreciation rate δ_{k} and durables depreciation rate δ_{d}

In the study of China’s economic fluctuations in the literature, the average life span of China’s fixed asset is mostly set at 10 years, the capital depreciation rate is 0.1, and the corresponding quarterly value is 0.025 [

3) Substitution parameters ρ_{c}, ρ_{y}, ρ_{F}, ρ_{x}

Using data from the US and Japan respectively, Pakos (2011) show that elasticity of substitution between durables and non-durables is close to 1, i.e., ρ c = 0 [

4) Share parameter α_{y}

We choose α y = 0.5 as in He et al. (2009). A combination of steady-state values and other parameters can pin down the other three share parameter values without calibration.

5) Investment adjustment cost parameters ϕ_{k} and ϕ_{d}

The larger the values of ϕ k and ϕ d , the greater the adjustment costs of investment of capital and durables, or vice versa, and when the value is 0, adjustment costs do not exist. Compared to ϕ k = 1 in Atkeson and Kehoe (1999) for the US economy, we set the two parameters as 3 in terms of China as a developing country with the incompleteness of financial markets.

6) Labor supply elasticity η

There are few Chinese empirical researches on the setting of η and the results differences are also large, but in the RBC literature, its value is generally set to 1, and we also choose this value.

7) Steady-state value (K/Y, N/Y, I_{D}/N, O_{h}/N, K/O_{f})

To solve the differential equations system after log-linearization, five more steady-state values are needed to determine. According to (5), when it’s steady-state there is K = I_{K}/δ_{k}, then to calculate the mean capital investment data in the sample period, and the steady-state capital value K can be figured out when combining the previously calibrated capital depreciation rate. When utilizing mean data related to the output, durables investment, household oil consumption, non-durables consumption in the sample period, it is easy to obtain K/Y of 22, N/Y of 0.2, I_{D}/N of 0.61, and O_{h}/N of 0.31. In addition, as it is impossible to get oil consumption data from China firms, K/O_{f} = 300 is set with a reference of the estimation of the US economy by Kim and Loungani (1992). The differences of the capital accumulation and the level of economic development between Sino-US at this stage may be of nearly three decades, so the value set also has certain rationality.

In conclusion, all deep parameters of RBC model are summarized in

Toolkit package containing Matlab source code by Uhlig (1999) is used to obtain cyclical characteristic information for each macroeconomic variable in “Second

β | δ k | δ d | α y | η | ϕ k | ϕ d | ρ F | ρ x | ρ c | ρ y |
---|---|---|---|---|---|---|---|---|---|---|

0.99 | 0.025 | 0.025 | 0.5 | 1 | 3 | 3 | 0.7 | 3 | 0 | 0 |

ρ A | ρ o | ρ u | σ A | σ o | I D N | O h N | K Y | K O f | N Y | |

0.8 | 0.49 | 0.57 | 0.03 | 0.12 | 0.61 | 0.31 | 22 | 300 | 0.2 |

Moment” after the model log-linearization, and the results are shown in Tables 4-8. For comparison purposes, it is treated as follows:

1) RBC model with durable goods consumption is taken as a benchmark model in this paper, and there exist two shocks (oil price and technology) which are denoted as DRBC.

2) Model structure is the same with 1), but with only the oil price shocks, denoted as DRBC-OIL; the purpose is not to investigate changes in the technology, but only to discuss the impact on the business cycle of oil price shocks.

3) Model structure is the same with 1), but with only technology shocks, denoted as DRBC-TFP; the purpose is not to investigate changes in oil price, but will only discuss the impact on the business cycle of technology shocks.

4) It contains RBC model with a single consumption structure, namely, a simple RBC type model, which means consumption is not distinguished between durables and non-durables, and also with two shocks, denoted as SRBC.

5) Model structure is the same with 4), but with only the oil price shocks, denoted as SRBC-OIL.

6) Model structure is the same with 4), but with only technology shocks, denoted as SRBC-TFP.

When introducing consumer durables into oil economy of RBC model, there are three questions to be answered: first, compare directly the artificial DRBC model (benchmark model) with the actual economy to see if it better predicts China’s RBC? Second, compared with the standard oil economy model SRBC, are the predictions of DRBC benchmark model obviously improved? Third, compared to traditional RBC model which considers technology as the most important source of economic fluctuations, what kind of role is oil price shock playing in the business cycle, what impact differences on the core macroeconomic variables such as output and consumption, what is the transmission mechanism?

The predicted results of DRBC, DRBC-OIL and DRBC-TFP are shown in

From the point of volatility, the standard deviations of oil price and household oil consumption are 14.98% and 10.09% respectively, far greater than the volatility of output 3.75%, 4.00 times and 2.69 times of the output respectively; capital investment, total investment, durables investment are also higher than that of output, namely, 5.60%, 5.39% and 5.05%; output is ranked No. 6, and labor and consumption are low, with only 1.69% and 1.61%, of which consumption volatility the lowest reflects exactly the classical theory of household intertemporal smooth consumption behavior advocated by RBC^{6}. Priorities of this volatility

Variable | Actual economy | Artificial economy (DRBC) | |||||
---|---|---|---|---|---|---|---|

Standard deviation (%) | Autocorrelation | Correlations with output | Standard deviation (%) | Autocorrelation | Correlations with output | K-P ratio (%) | |

Output | 3.76 | 0.39 | 1.00 | 3.75 | 0.48 | 1.00 | 99.73 |

Consumption | 1.74 | 0.71 | 0.15 | 1.61 | 0.48 | 0.18 | 92.53 |

Capital investment | 5.93 | 0.50 | 0.78 | 5.60 | 0.47 | 0.98 | 94.44 |

Durables investment | 5.28 | 0.59 | 0.52 | 5.39 | 0.40 | 0.63 | 102.08 |

Total investment | 5.19 | 0.61 | 0.88 | 5.05 | 0.50 | 0.99 | 97.30 |

household oil consumption | 7.96 | 0.75 | 0.04 | 10.09 | 0.48 | 0.07 | 126.76 |

Labor | 2.45 | 0.49 | 0.74 | 1.69 | 0.48 | 0.89 | 68.98 |

Oil price | 20.73 | 0.69 | 0.06 | 14.98 | 0.48 | -0.04 | 72.26 |

Note: Simulation results are average over 10000 simulations each with length 77 quarters, which is the same sample number of periods as the China sample. The K-P ratio denotes the ratio of standard deviation of artificial economy to that of actual economy, after using the HP filtering method proposed by Kydland and Prescott (1982). (Similarly for Tables 5-7).

Variable | Actual economy | Artificial economy (DRBC-OIL) | Artificial economy (DRBC-TFP) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Standard deviation (%) | Auto- correlation | Correlations with output | Standard deviation (%) | Auto- correlation | Correlations with output | K-P ratio (%) | Standard deviation (%) | Auto- correlation | Correlations with output | K-P ratio (%) | |

Output | 3.76 | 0.39 | 1.00 | 0.99 | 0.66 | 1.00 | 26.33 | 4.27 | 0.64 | 1.00 | 113.56 |

Consumption | 1.74 | 0.71 | 0.15 | 1.58 | 0.67 | 0.98 | 90.80 | 0.45 | 0.77 | 0.76 | 25.86 |

Capital investment | 5.93 | 0.50 | 0.74 | 0.69 | 0.14 | −0.76 | 11.64 | 6.50 | 0.64 | 0.99 | 109.61 |

Durables investment | 5.28 | 0.59 | 0.52 | 4.22 | 0.40 | 0.89 | 79.92 | 3.98 | 0.67 | 0.99 | 75.38 |

Total investment | 5.19 | 0.61 | 0.88 | 0.26 | 0.71 | 0.99 | 5.01 | 6.04 | 0.64 | 0.99 | 116.38 |

Household oil consumption | 7.96 | 0.75 | 0.04 | 10.05 | 0.67 | 0.99 | 126.26 | 0.50 | 0.75 | 0.82 | 6.28 |

Labor | 2.45 | 0.49 | 0.78 | 0.63 | 0.62 | −0.98 | 25.71 | 1.81 | 0.64 | 0.99 | 73.88 |

Oil price | 20.73 | 0.69 | 0.06 | 14.93 | 0.67 | 0.99 | 72.02 | 0 | 0.86 | 0.59 | 0 |

completely coincide with the actual economy.

From the point of view of K-P ratio, the output volatility of DRBC is close to data from China, with its output K-P ratio reaching 0.9973, indicating that the model accounts for 99.73% of the volatility of output in the data.

From the point of view of the correlations with output, the model DRBC shows that all series are pro-cyclical, except for oil prices, which is weakly countercyclical. The DRBC predicts this dimension closely. In particular, the correlations of labor, capital investment, the total investment and output are up to 0.99, 0.98, and 0.89 respectively, higher than in the actual economy, showing a strong pro-cyclicality. The correlation between durables investment and output is 0.63, slightly higher than 0.52 in the actual economy. As mentioned earlier, compared with the developed economies, China’s consumption is weakly pro-cyclical, and DRBC better captures the feature, with the correlation between consumption and output in the artificial economy being 0.18, not far from 0.15 of the actual economy^{7}. The correlation between household oil consumption and output is 0.07, close to 0.04 of the actual economy, showing a weak counter-cyclicality. The model underestimates the cyclicality of oil prices to output ratio and obtains −0.04, as opposed to 0.06 in the actual economy, nevertheless both closer to 0. The predicted correlations with output in the artificial economy are consistent with the actual economy in order.

From the point of view of the autocorrelations, the autocorrelations of variables of DRBC have shown a positive correlation, exhibiting persistency, which are also more matching with the actual economy.

In summary, the DRBC model can accurately simulate the “Second Moment” feature about the actual economy, and can be used as an appropriate model to capture the volatility of China’s economy.

Simulated results that do not consider the consumer durables of SRBC, SRBC-OIL, and SRBC-TFP are shown in

Starting with consumption comparison, volatilities in consumption prediction by DRBC (1.61%) are greater than that of SRBC (0.68%), closer to the actual economy (1.74%). Furthermore, with regard to the K-P ratio, the explanatory power of DRBC of 92.53% is much higher than SRBC of 39.08%; Eventually, SRBC shows a strong pro-cyclicality for consumption (a correlation between consumption and output is 0.84), which cannot fit a weak pro-cyclical consumption characteristic of China’s actual economy, whereas DRBC can better fit the characteristics.

From the output comparison, SRBC predicts the standard deviation of output

Variable | Actual economy | Artificial economy (SRBC) | |||||
---|---|---|---|---|---|---|---|

Standard deviation (%) | Autocorrelation | Correlations with output | Standard deviation (%) | Autocorrelation | Correlations with output | K-P ratio (%) | |

Output | 3.76 | 0.39 | 1.00 | 3.72 | 0.48 | 1.00 | 98.94 |

Consumption | 1.74 | 0.71 | 0.15 | 0.68 | 0.48 | 0.84 | 39.08 |

Capital investment | 5.93 | 0.50 | 0.74 | 6.03 | 0.49 | 0.99 | 101.69 |

Durables investment | 5.28 | 0.59 | 0.52 | NA | NA | NA | NA |

Total investment | 5.19 | 0.61 | 0.88 | NA | NA | NA | NA |

Household oil consumption | 7.96 | 0.75 | 0.04 | NA | NA | NA | NA |

Labor | 2.45 | 0.49 | 0.78 | 1.64 | 0.48 | 0.92 | 66.94 |

Oil price | 20.73 | 0.69 | 0.06 | 14.98 | 0.47 | 0.04 | 72.26 |

Note: NA denotes Undefined (Similarly hereinafter).

Variable | Actual economy | Artificial economy (SRBC-OIL) | Artificial economy (SRBC-TFP) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Standard deviation (%) | Auto- correlation | Correlations with output | Standard deviation (%) | Auto- correlation | Correlations with output | K-P ratio (%) | Standard deviation (%) | Auto- correlation | Correlations with output | K-P ratio (%) | |

Output | 3.76 | 0.39 | 1.00 | 0.99 | 0.65 | 1.00 | 26.33 | 4.23 | 0.64 | 1.00 | 112.50 |

Consumption | 1.74 | 0.71 | 0.15 | 0.29 | 0.40 | −0.99 | 16.67 | 0.81 | 0.71 | 0.93 | 46.55 |

Capital investment | 5.93 | 0.50 | 0.74 | 0.34 | 0.39 | 0.99 | 5.73 | 7.08 | 0.64 | 0.99 | 119.39 |

Durables investment | 5.28 | 0.59 | 0.52 | NA | NA | NA | NA | NA | NA | NA | NA |

Total investment | 5.19 | 0.61 | 0.88 | NA | NA | NA | NA | NA | NA | NA | NA |

Household oil consumption | 7.96 | 0.75 | 0.04 | NA | NA | NA | NA | NA | NA | NA | NA |

Labor | 2.45 | 0.49 | 0.78 | 0.64 | 0.61 | 0.97 | 26.12 | 1.74 | 0.64 | 0.99 | 71.02 |

Oil price | 20.73 | 0.69 | 0.06 | 14.93 | 0.66 | 0.93 | 72.02 | 0 | 0.86 | −0.60 | 0 |

as 3.72%, almost the same level with DRBC, close to 3.76% in the actual economy, and thus these two models are also similar in explanatory power of the K-P ratio. Actually in

From investment and labor, the standard deviations of these two series for SRBC are 6.03 and 1.64 respectively. When compared with the actual economy, DRBC is slightly better than SRBC in volatility forecasting. Investment volatility in SRBC increases mainly due to the lack of smooth durables investment, and households only rely on capital investment portfolio rebalanced, resulting in increased investment volatility. In

^{8} are introduced in the model: one is technology shocks, the core of RBC theory, the

Variables Shocks | Output | Consumption | Capital investment | Durables investment | Total investment | Household oil consumption | Labor |
---|---|---|---|---|---|---|---|

Technology shocks | 96.3 | 64.9 | 99.3 | 65.2 | 99.8 | 4.6 | 90.4 |

Oil price shocks | 3.7 | 35.1 | 0.7 | 34.8 | 0.2 | 95.4 | 9.6 |

other one is oil price shocks, the theme of this paper. Variance decomposition results clearly show the extent of the impact of exogenous shocks on macroeconomic variables volatilities. It can be seen that the impact of oil price shocks is reflected in three variables, namely, consumption, durables investment and household oil consumption. Among them, the oil price shocks account for 35.1% of consumption volatility, 34.8% of durables investment volatility, 95.4% of household oil consumption volatility; oil price shocks account for less than 10% of volatility on output^{9}, investment, total investment and labor, which means that most of the volatilities are derived from technology shocks, and especially technology shocks account for 96.3% of the output, which is almost consistent with the traditional RBC theory that technology shocks can account for 100% of output volatility approximately.

In short, from the variance decomposition it can be found that output, investment and labor volatilities in this model are mainly dominated by technology shocks, and oil price shocks mainly affect consumption volatility, also can verify the conclusions made from Tables 4-7.

determine capital demand), therefore, it can be drawn that households need to rebalance its investment portfolio for durables and capital goods. According to the calibration study, in the initial steady state, the proportion between household oil and durables (O_{h}/D = 0.013) is much larger than the ratio of oil to capital in production (O_{f}/K = 0.003). The decline in marginal revenue of durables caused by oil price shocks is higher than the marginal revenue decline of capital goods. In order to balance the marginal income differences, households will immediately rebalance the portfolio, increase capital goods while reducing durable goods, and this capital increase will sufficiently offset the decrease in firms’ demand of capital investment brought by high oil prices; meanwhile the ARMA (1, 1) of the oil price shocks determines that the propagation of oil price shocks is characterized by two periods in the time dimension, which together leads to a two-periods increase in capital investments (i.e., greater than zero). Then starting from the third period, capital investment is switched into a negative trend, mainly because the high capital stocks K t and low durables stocks D t in the initial period have led to the fact that the portfolio rebalanced behavior of households cannot fundamentally reverse the huge gaps between those two, therefore, produce subsequent negative trends for two types of investment. The rise of capital and labor has increased the production, but brought forth the decline in the value added V A t because the decline in durables investment and non-durables is greater than the short-term increase in the magnitude of capital investment.

Unlike oil price shocks, technology shocks have a direct impact on production function, but do not enter the utility function and do not directly influence durables investment. Therefore technology shocks do not affect the two portfolio reallocation by households, just leading to the rise in capital investment. Since our purpose is to study the impact of oil prices, and the impact mechanism of technology on the economy has been extensively studied in a large number of RBC literatures, it will not be discussed here due to limited space.

Existing literatures on China’s RBC focus on the impact of macroeconomic cycle brought by technology, finance, monetary, international credit, and sunspot shocks, but lack discussion on energy price shocks represented by oil, and ignore the fact that the international oil price volatility in recent years is one source of external shocks of China’s economic fluctuations. Especially in the past two decades, international crude oil prices are violently fluctuated within a wide range of repeated shocks between $ 20/barrel and $147/barrel, and early in 2011, China’s dependence on foreign oil overtook that of the United States, being the world’s number one. In view of this, we build oil economy RBC model with durables consumption, simulation and forecast, combining with economic data of 1997Q1 to 2016Q1 in China, with the following discoveries:

First, it is important to divide the RBC model into consumer durables and non-durables when studying China’s economic fluctuations. According to the simulation results of model DRBC with consumer durables, the core finding is DRBC has improved consumption volatility and weak pro-cyclicality predicted closer to the actual economy. On one hand, the traditional SRBC containing oil price shocks can account for only about 40% of consumption volatility, while DRBC increases the explanatory power to more than 80% of the volatility; on the other hand, SRBC shows a strong pro-cyclicality and cannot predict the weak pro-cyclicality of China’s actual economy, whereas DRBC can fit the feature.

Second, the oil price shocks mainly affect consumption volatility, but seldom influence output, investment and labor, the three variables of which are largely influenced by technology shocks. Specifically, the K-P ratio of consumption in DRBC-OIL is up to 90.80%, while K-P ratio of that in DRBC-TFP is only 25.86%; the K-P ratios of output, investment and labor in DRBC-TFP are 113.56%, 109.61%, and 73.88% respectively, while in DRBC-OIL the corresponding ratios are 26.33%, 11.64%, and 25.71% respectively.

Third, the benchmark model (DRBC) reveals that the transmission mechanism of oil prices is determined by intra-temporal income effects and inter-temporal effects of portfolio rebalanced between durable goods and capital goods.

It is implicated that the impact of oil price shocks on China’s output volatility may not be so big, but the main impact is on consumption. Expanding domestic demand and boosting consumption become the main tone in the future of China’s economic transition and growth; therefore great importance should be attached to the impact of oil price shocks on consumption levels.

This work was supported by the Project of the National Social Science Fund of China [grant numbers: [15CJY064].

The authors declare no conflicts of interest regarding the publication of this paper.

Wang, Y.Q.., Sui, X.Y. and Pan, W.J. (2019) Oil Price Shocks, Durables Consumption, and China’s Real Business Cycle. Modern Economy, 10, 1310-1333. https://doi.org/10.4236/me.2019.104089