Uncertainty and risk analysis of the Langrun Chinese GDP Forecast: Fan Charts revisited

Abstract

In this paper, we develop a fan chart methodology for Chinese economic growth to incorporate uncertainty analysis into the gross domestic product growth forecast. Using the ‘Langrun Forecast’ project results exclusively, we estimate the density distribution for Chinese gross domestic product growth forecasts and build corresponding fan charts for the first time. Our analysis shows that the fan chart method effectively highlights the overall uncertainty and balance of risks surrounding Chinese gross domestic product growth, especially during the past international financial crisis between 2007 and 2009. Wallis' interval forecast test is conducted to evaluate the performance of the produced fan charts, and the results indicate that our forecasts perform well for the period being investigated.

Keywords:

• Fan chart
• balance of risks
• economic forecast
• Chinese GDP growth rate
• Langrun Forecast

JEL Classification:

• C82
• E37
• O53

Notes

1. More precisely, Clements and Hendry (1998) elaborately categorized five sources of model-based forecast error, which can be emerge into these two main aspects as concluded by Hendry and Ericsson (2001).

2. See Appendix A for more details of the relation between a TPN distribution and the two component normal distributions.

3. As for the skewed normal distribution, for example, except for mean and variance, two other parameters (a location parameter and a scale parameter) have to be estimated in order to determine the distribution completely. Comparatively, only three parameters (mode and two variances for the two component normal distributions) need to be estimated to determine a TPN distribution.

4. Blix and Sellin (1999) have applied the three methods mentioned here to display the same inflation density forecasts made by the Riksbank.

5. Individual density forecasts could also be aggregated to form comprehensive density forecast according to designed schemes. In a recent paper, Kenny, Kostka and Masera (2011) proposed a framework to investigate the information content of subjective expert density forecasts and corresponding aggregated density forecast using micro data from the ECB's Survey of Professional Forecasters. Due to lack of density forecast results, only point forecasts are used in this paper to estimate the density forecast for Chinese GDP growth rate.

6. Compared with the original formula introduced by Elekdag and Kannan (2009), we simply drop the covariance between ‘risk factors’, not only because of the difficulty to determine their value but also due to the fact that they are simply dropped out when the authors calculated φ in practice.

7. Because an important feature of market participants is forward-looking, much information for future uncertainty might be exploited from market behaviors. The research in this field is growing rapidly in recent years. For example, Bahra (1997) summarized the early efforts to extract implied risk-neutral probability density functions from option prices, Ält-Sahalia and Duarte (2003) developed a more advanced nonparametric approach for the same purpose.

8. The regularly forecasted indices include quarterly growth rates of GDP, consumer price index (CPI), industrial value-added, investment, consumption, export and import, interest rate and exchange rate. The list of participating institutes has grown from 14 members in the first exercise to 22 members in the 24th exercise (forecast for the second quarter of 2011) and might probably continue to increase. Participating institutes of this project (containing those which have once participated but later quitted) include Bank of China International Securities Essences Securities, Bank of Communications, Guotai Junan Securities, Blue Oak Capital, HSBC, BNP Paribas, Industrial and Commercial Bank of China, China Center for Economic Research Peking University, Institute of Quantitative & Technical Economics Chinese Academy of Social Sciences, China Galaxy Securities, Merrill Lynch, China International Capital Corporation Limited, Morgan Stanley, China Merchants Securities, Nomura Securities China Securities Co., Shenyin Wanguo Securities, Citibank, Standard Chartered Bank, CITIC Securities, UBS, Department of Economic Forecasting State Information Center, Unirule Institute of Economics, Essence Securities, Greatwall Securities and China Securities Co. The historical forecasting data could be found at http://www.nsd.edu.cn/cn/list.asp?classid=634# (in Chinese).

9. Despite being easy to handle with, this weighting method is fairly rough and has potential to be improved. Plenty of work has been done in this field. For example, Clark and McCracken (2009) use Monte Carlo experiments to decide whether the recursive and rolling schemes or a scalar convex method should be used for combination, especially when linear predictive models are subject to structural change. Hsiao and Zhao (2000) explored the usefulness of opinion surveys with time-series data. For general principal for forecast combination and a brief review of early forecast combination methods, see Palm and Zellner (1992).

10. Note that, quantitatively, a negative skew indicates that the tail on the left side of the probability density function is longer than the right side and the bulk of the values (including the median) lie to the right of the mean. A positive skew indicates an exactly opposite situation.

11. Elekdag and Kannan (2009) focused on the term spread and the Standard and Poor's (S&P) 500 index in order to estimate the impact of financial conditions on world economy growth. Given the high representativeness of the stock market in United States and high correlation of the financial markets among major developed countries, such financial condition is a good indicator for uncertainty estimation. Considering that major developed countries contribute more than 70% of world GDP but are relatively vulnerable to shocks in oil market, oil price risk should also be highly relevant to the total uncertainty surrounding global economy growth.

12. As an illustration of price control, the National Development and Reform Commission (NDRC) has long been regulating the domestic price of petroleum product, and Chinese domestic oil price adjustment is usually lagging the international price fluctuation in time and less so much in scale.

13. According to the description of The Conference Board, CBCI is a composite index, the components of which include Value Added of Industrial Production, Retail Sales of Consumer Goods, Electricity Production, Volume of Passenger Traffic and Manufacturing Employment. More information of this indicator could be found at the official website www.conference-board.org.

14. The importance of net export to Chinese GDP could be measured by the ratio of total foreign trade value to GDP. This ratio has increased steadily during the last decade, from 36% in 1999 to approximately 50% in 2010.

15. The incremental contribution of the ‘risk factors’ is also tested to be significant. The p-value of F-test that such ‘risk factors’ has no effect on the fluctuations of GDP growth rate is lower than 0.001.

16. Since late 1990s, many scholars have raised increasing doubts about the quality of China's official statistic data, especially the key indicators like GDP and its growth rate, as well as CPI inflation. Some scholars believe that Chinese governments, especially provincial and local governments, tend to exaggerate the GDP level and its growth rate to show off their political achievements. Krugman (2011) even claimed that China's statistic numbers ‘are more fictional than the most boring form of science fiction’. The criticisms of Chinese official statistic quality mainly focus on the inconsistency of GDP growth rate and other key indicators which are believed to relate closely to and move at a similar pace with GDP growth rate, such as energy consumption and railway traffic volumes (Rawski 2001a, b; Sinton 2001). On the other hand, however, some scholars still have cautious faith in China's official statistic data. In a very influential empirical study, Klein and Özmucur (2002) examined some strategic indicators that are suggested by basic social accounting principles and concluded that principal components of these indicators indeed reflect the movement of official estimates of the Chinese economy. They further indicated that, in fact no one knows the correct estimate, and the key point lies in the way how the estimate is calculated, which is true not only to China but the world wide over. Following Klein and Özmucur's (2002) opinion, I leave this controversial problem aside and still use official data as benchmark to evaluate the accuracy of forecasts. Another reason for using official data is the self-adaption of forecasters of Chinese economy. It is reasonable to believe that the inherent sources which may cause measurement error in official GDP growth rates might probably also affect forecasters of Chinese economy in a similar pattern, because the forecasters have to make their forecast results as close to the official data as possible to show their prediction ability when no more reliable statistic data are available.

17. Two of the classical methods of testing density forecast, namely the likelihood ratio and Pearson chi-squared tests, are conducted through dividing the range of the variable into several mutually exclusive classes and then comparing the probabilities of actual outcomes that fall into these classes with the theoretical value. By doing so the density forecast tests are essentially degraded to interval forecast tests.

18. Notice that our tests here are only for the overall uncertainty of constructed fan charts, leaving the accuracy of forecasted balance of risks untouched.

19. For example, during the whole 2009 and the first quarter of 2010, when was the main period of the ongoing world financial crisis, the intervals are obviously wider than other time. The confidence interval by indirect estimation approach in the first quarter of 2010 is considerably wide, reflecting the huge dispersion of forecasts for key influential variables due to the turbulence triggered by the unprecedented GDP growth rate slowdown from 9% in the third quarter of 2009 to 6.8% in the fourth quarter of 2009.

20. This appendix is adapted from Box 1 and section II of Elekdag and Kannan's (2009) paper.

21. The criterion for real roots of the quadratic Equation (B.1) is , which can be satisfied in a normal case so we ignore the possibility of complex roots, although it is not totally impossible theoretically.

22. Wallis (1999) has discussed another approach for constructing confidence interval, that is, to make equal tail probabilities of the interval: Pr(x < a) = Pr(x > b) = (1−p)/2. Interestingly, he argued that this constructing method is theoretically superior to the shortest interval method we applied because the loss function implied in the former approach is more reasonable than the ‘all-or-nothing’ loss function implicit in the latter.