3.1. Framework
Standard VAR modelling suffers from four main drawbacks (see Bernanke et al. 2005, among others). First, it requires a plausible identification of shocks and many authors have disagreed about the appropriate strategy for identifying those shocks (Bernanke and Mihov 1998; Christiano et al. 2000). Second, to conserve degrees of freedom, standard VAR are generally lowdimensional in the sense that they include a small number of variables. This small number of variables is unlikely to account for all the information representative of the Chinese economy. Third, because the number of variables is limited, the considered variables must precisely reflect their theoretical counterparts. As illustrated by Bernanke et al. (2005), for instance, the concept of ‘economic activity’ may not be exactly represented by GDP or industrial production or any other observed variable. Moreover, many observed variables are subject to revisions and are never free of measurement errors. Fourth, impulse responses issued from standard VAR modelling can be observed only for the included variables, which represent only a small fraction of variables that the researcher or policymaker cares about. To circumvent these problems, we follow Bernanke et al. (2005) by considering an approach that combines the standard VAR analysis with factor analysis, and proceed to the estimation of FAVAR models.^{8} The underlying idea is that a large amount of information about the economy can be summarized by a relatively small number of factors that stand in for broad economic concepts. As a consequence, to solve the degrees of freedom issue in standard VAR models, the usual VAR can be augmented with estimated factors. This enables us to exploit more information and to obtain the responses of a large set of variables to exogenous innovations.
Moreover, the ability of FAVAR models to deal, at least partly, with measurement errors is particularly beneficial for our study on China considering the lack of accuracy of the series: Chinese statistics are frequently criticized for their poor quality.^{9} Besides, given the unavailability of quarterly data for some indicators, we have to use interpolated series (see infra).
 (1)
 X_{t} =Λ^{f}F_{t} +Λ^{y}Y_{t} + u_{t},(2)
where Y_{t} is an M × 1 vector of the observed macroeconomic variables, including oil prices, X_{t} is an N × 1 vector of informational time series (with N large), F_{t} is a K × 1 vector of unobserved factors (with K being small) that summarize the information in X_{t}, ɛ_{t} is the error term with mean zero. Φ(L) is a lag polynomial of order d, Λ^{f} denotes an N × K matrix of factor loadings, Λ^{y} is an N × M matrix and u_{t} is an N × 1 vector of error terms supposed to be mean zero and uncorrelated (or weakly correlated).
The unobserved factors, F_{t}, might be seen as diffuse concepts, such as ‘economic activity’ or ‘price level’ that cannot be perfectly represented by one or two series but rather emerge in a wide set of economic variables. Because these F_{t} factors are not observable, equation 1 cannot be estimated directly. This is why a second equation is added: equation 2 supposes that the unobserved factors and the observed variables, Y_{t}, are linked to various economic time series that are grouped into X_{t}, the vector of informational time series. Therefore, this equation states that both vectors F_{t} and Y_{t} are common forces that drive the dynamics of X_{t} (see Bernanke et al. 2005).
If all the variables are assumed to be perfectly observed, then Y_{t} includes all these variables and F_{t} equals the null set. In this case, equation 2 is useless and the FAVAR model reduces to a standard VAR model. However, as previously mentioned, perfect observation is a strong assumption and, as a consequence, the FAVAR model is more realistic than the VAR one. As argued by Bernanke et al. (2005) among others, one might consider that almost all macroeconomic variables are not directly observed for two main reasons: existence of measurement errors (due to multiple rounds of revisions) and imperfect correspondence between theoretical concepts and specific time series. These arguments provide justifications for assuming that all macroeconomic variables, except the variable of interest, may be considered as unobservable. In this case, the vector F_{t} includes those macroeconomic variables and Y_{t} only contains the variable of interest.
The FAVAR model can be estimated in two ways. The first method, proposed by Stock and Watson (2002), relies on a twostep principal components approach and the second is based on a single step Bayesian likelihood method. As noticed by Bernanke et al. (2005), it is not clear which method dominates the other. We retain here the principal components method because it has the advantage of computational simplicity compared to the other procedure. In the first step, we use equation 2 to estimate the vector F̂_{t} of unobserved factors F_{t} using the principal components analysis (i.e. the first K principal components of X_{t}). In the second step, we estimate the FAVAR model (eqn 1) using standard methods and replacing F_{t} by F̂_{t}.^{10}
3.2. Selection of variables and model construction
We consider quarterly data for China over the 1980–2006 period. To summarize Chinese economic activity, we rely on the following macroeconomic variables: GDP, CPI, producer price index (PPI), households’ consumption, investment, imports, exports, 1year interest rates (lending and deposit), money supply (M2) and unemployment rate. These variables are usual indicators for the business cycle. Notably, they cover the main transmission channels reviewed previously (see Section 2). They were also chosen for practical considerations in the sense that they were available for our considered period.^{11} Data concerning price indexes, imports, exports, interest rates and money supply are extracted from the IMF International Financial Statistics. All other data are taken from the World Bank World Development Indicators. All these data are seasonally adjusted.
Turning to energy prices, we consider the crude oil price on the international market but also two other series: the PPI for coal and for electricity. Despite the regulation of energy prices in China, our variable of interest is the price of oil on international markets. Indeed, our purpose is to test whether oil prices affect the Chinese economy in spite of the state control. As explained before, this might be the case because: (i) oil price increases in international markets are partly passed through to consumer prices, most of the time, in our sample; (ii) the financial resources of oil firms and the government devoted to the subsidization of energy products could be used more efficiently; and (iii) the regulation leads to serious dysfunction (notably shortages). In relation to the first point, it seems interesting to consider PPI for other energy products as well, in order to analyze the transmission of an oil price change. We focus on coal and power due to the specific energy situation of China. Indeed, China's energy balance is dominated by coal, despite the move towards oil products, whereas demand for power is rapidly growing for both industrial and residential usages. Annual price data series were extracted from the China Statistical Yearbook^{12} and have been converted into quarterly frequency using cubic spline interpolation. It would have been desirable to include consumer prices too, but, unfortunately, to the best of our knowledge, such series are not available^{13} (retail prices for gasoline can be found from 1994, which constitutes too short a sample).
We consider series in real terms to remove the specific impact of inflation that may cause spurious common behaviour among series. Consequently, all macroeconomic time series but interest rates, price indexes and unemployment rate are expressed in constant RMB. Interest rates and energy price indexes are expressed in real terms, using the CPI as a deflator. All series except interest and unemployment rates have been transformed in logarithm.
We first proceed to the application of standard unit root tests (Dickey and Fuller 1979, 1981; Phillips and Perron 1988; Kwiatkowski et al. 1992) on real series. The first two tests are based on the null hypothesis of a unit root, while the Kwiatkowski, Phillips, Schmidt and Shin test considers the null of no unit root. With some exceptions, all our considered series appear to be integrated of order one, which is a standard result in the published literature for such series.^{14}
To pursue the preliminary analysis, we perform bivariate Granger causality tests as well as examine the interactions in our set of variables.^{15} Three main conclusions emerge. First, international oil prices can be considered as exogenous between 1980 and 2006. Considering the growing share of China in global oil consumption, this result should not last for long: the causality from GDP to oil prices becomes marginally significant at the 10% level, which is consistent with the conclusion of Zhao and Wu (2007, p. 4245), who argue that China is ‘a large country in the international market and its trade behavior thus can influence the international price’. Second, PPI for energy are influenced both by international oil prices (as expected, considering the leading role played by oil prices on the international energy markets) and by national macroeconomic variables. Third, many causal relationships exist from energy prices to macroeconomic variables. On the whole, the energy price series that causes the majority of macroeconomic series is the coal one, confirming the importance of coal in the Chinese economy.
Turning now to the FAVAR construction and following the arguments by Bernanke et al. (2005) concerning the choice between observable and unobservable variables, only the international crude oil price is included in the vector Y_{t}. The vector X_{t} includes the following variables: GDP, CPI, PPI, households’ consumption, investment, imports, exports, lending rate, deposit rate, M2, unemployment rate and producer price indexes for coal and electricity. Furthermore, we include the GDP of OECD countries^{16} as an exogenous variable in the FAVAR model to account for the potential impact of the rest of the world on the Chinese economy. Indeed, the Chinese industry is highly oriented towards exportation and it would be important to not neglect the influence of foreign economic activity. All the series were considered in real terms and have been transformed to induce stationarity.
3.3. Empirical implementation and results
When estimating a FAVAR model, the length of the autoregressive structure and the number of factors included in the VAR have to be determined. Following Bernanke et al. (2005), we checked the empirical plausibility of a large variety of specifications to select our reference model. Note that our choice of the autoregressive structure has been guided by usual information criteria. Following Hamilton and Herrera (2004), who show that autoregressive models with fewer than eight lags for quarterly data are unable to correctly account for the oil price influence, we rejected such parsimonious autoregressive structures and selected the model that minimizes Akaike and Schwarz information criteria among specifications with eight lags or more. The most successful specification appears to be the VAR(8) with five factors, including contemporaneous and eight lagged values for the OECD GDP.^{17}
As noted by Bernanke et al. (2005), the factors estimated by principal components might be shown to stand in for broad concepts like ‘economic activity’, ‘price level’ or ‘credit conditions’. The matrix of eigenvectors that reports the linear relationships between the principal components and the informational variables enables us to interpret the factors. Table 1 shows the principal components decomposition of our group of variables.^{18}
Table 1. Principal components analysis  Component 1  Component 2  Component 3  Component 4  Component 5  Component 6  Component 7 

Eigenvalue  3.63  2.38  1.7  1.44  0.99  0.89  0.77 
Variance proportion  0.28  0.18  0.13  0.11  0.08  0.07  0.06 
Cumulative proportion  0.28  0.46  0.59  0.7  0.78  0.85  0.91 
Eigenvectors 

Variable  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7 


GDP  0.46  –0.08  –0.06  –0.14  –0.03  –0.06  0.12 
Investment  0.4  –0.31  0.12  –0.2  –0.02  –0.04  0.16 
Consumption  0.33  –0.17  –0.33  –0.33  –0.22  –0.26  0.02 
Unemployment  0.01  0.25  0.48  –0.02  0.43  0.02  0.5 
M2  0.02  –0.21  –0.01  –0.21  0.75  –0.34  –0.46 
Exports  0.01  –0.13  0.01  0.68  –0.1  –0.27  –0.32 
Imports  0.16  –0.2  –0.11  0.46  0.14  –0.43  0.52 
Lending rate  –0.43  –0.12  0.1  –0.22  –0.19  –0.4  0.12 
Deposit rate  –0.42  –0.11  0.12  –0.22  –0.17  –0.41  0.12 
CPI  0.23  0.51  0.13  –0.02  –0.11  –0.33  –0.14 
PPI  0.23  0.42  0.33  –0.04  –0.19  –0.31  –0.21 
PPI for power  0.09  –0.35  0.52  0.06  –0.05  0.12  –0.16 
PPI for coal  0.1  –0.36  0.46  –0.03  –0.24  0.05  –0.09 
Basically, the first factor could be seen as an indicator of ‘real economic activity’ in a broad sense. The second factor might reflect essentially the ‘overall price level’. The third one seems to express mainly the ‘relative producer price level for other energy resources’ (as well as unemployment, surprisingly). The fourth factor is related to ‘trade activity’ and the fifth one may reflect ‘unanticipated changes in money supply’ (through its strong positive correlation with M2 and its negative correlation with real activity and price measures). The remaining factors are more difficult to explain. Of course, these interpretations are simplistic and subject to debate.
To investigate the mechanisms of propagation of an oil price increase through the Chinese economy, we evaluate generalized impulseresponse functions (Pesaran and Shin 1998) for the estimates of the unobserved factors. The results are reported in Figure 1. Overall, oil price increases negatively affect real economic activity and exert an upward pressure on overall prices first, and then on relative producer prices for other energy resources. Despite the regulation of consumer prices for energy resources, international oil prices do affect the Chinese economy. As mentioned earlier, the influence might be indirect, through pernicious effects of shortages or through inefficient use of resources by oil firms and the government.
To assess more precisely the effects of an oil price increase on the Chinese economy, the impulse responses of the unobserved factors can be used to draw out the dynamic responses of any series among the informational variables. More specifically, the response of a variable X_{i}to a shock in the oil price is given by:
where ∂F_{kt}_{+j}/∂Y_{t} is the jperiod ahead response of estimated factor k (k = 1, . . . , K) to a shock in the international oil price. The weights λ_{i}, i = 1, . . . , N, are calculated using series standard deviations and eigenvectors given by the principal components analysis.
Figure 2 reports the results for the more interesting variables. Some appealing conclusions emerge. A positive oil price shock has a direct, shortlived, impact on PPI and CPI, which rise at first. This induces a monetary response: after a brief drop reflecting the rise in inflation, real interest rates go up (both the reported lending rate and the unreported deposit rate). Thus, the pressure on overall prices fades away quickly, whereas demand slows. The effects on GDP, investment and consumption are strongest in the second year after the shock.^{19} In contrast, unemployment is not significantly influenced by oil prices. This might be related to the fact that official unemployment figures are wellknown for being misleading, and notably for not capturing the severe underemployment in China. Imports and exports are not significantly affected as well, but the estimated impulse response coefficients suggest an improvement of the trade balance due to a slowdown in imports. Relative prices for power and coal increase. Their responses become significant in the third year following the oil price shock. This delayed impact reflects the natural transmission of an oil price variation to prices of other energy resources, as the substitution possibilities are limited in the very short run, but it presumably results from the regulation of energy prices as well, which acts against market forces.
As robustness checks, we finally perform other FAVAR estimations by varying the number of autoregressive lags and the number of included factors. Results were found to be rather insensitive to the choice of the length of the autoregressive structure, as long as it was not too short (typically, longer than four). Turning to the selected factors, the qualitative nature of the results was basically unaffected by changing the number of factors, but this leads to less significant responses, especially when the number of factors increases.