# **Sensitivity of the estimates to assumptions**

# **_General sensitivity with respect to depreciation_**

There are a large number of assumptions for both the depreciation rate and the initial capital stock in the literature. For depreciation, the estimates vary between 3% and 10%. A meta-regression for the 42 identified published estimates suggests that assumptions about the depreciation rate have drifted upwards over time: from 3% in 1988 to 7.2% in 2017, with an average for English language estimates of just over 5%, consistent with the international experience and with the estimates used in this paper. If the published paper is in Chinese, or directly cites Chinese sources, then the estimate of the depreciation is 3.4 percentage points higher than the estimates in English language papers.

Given these differences, the sensitivity of the capital stock estimated in this paper to different assumptions about the initial capital stock and depreciation rates has been estimated. The estimates of the capital stock in the past two decades are almost completely unaffected by estimates of the initial capital stock given the rapid growth of investment in China since 1952 and the impact of the depreciation of the initial capital stock over time. Indeed, a doubling of the capital stock in 1952 would raise the estimated level of the capital stock in 2016 by only 0.02%.

The estimated level of the capital stock is more sensitive to the depreciation rate than to the initial value of the capital stock. The extent of the dispersion in estimates of the capital stock using the perpetual inventory method depends on the growth rate of investment over the time period for which the capital stock is estimated as well as the depreciation rates. A high growth rate of investment moderates the difference in estimated capital stocks due to assumptions about depreciation to a significant extent. For example, with a 5% depreciation rate and zero investment growth, the estimate of the capital stock will eventually converge to be half the estimate with a 10% depreciation rate. However, if the annual compound growth rate of investment is 10% (close to the 63 year average growth in Chinese capital formation), the difference in the eventual level of the capital stock will be reduced to one-quarter (see Box 1 for the derivation of this result). Moreover, the convergence to the long-run difference will be much quicker with the 10% investment growth rate than with zero growth.

With the path of sectoral investment estimated in this paper, the difference in the levels of the capital stock had converged to close to their expected long-run values by 2005 (Figure 11, Panel A). The consequence of this quick convergence of the ratio of the different estimates of the capital stock to the estimate with 5% depreciation is that over the period 1995 to 2015, there is very little difference in the growth rates of the different estimates of the capital stock contingent on different depreciation rates. From 1998 onwards, the spread between the highest and lowest estimated growth rates is rarely greater than 0.5% (Figure 11, Panel B).

**Figure 11 Sensitivity of capital stock estimates to changes in the depreciation rate**

<!-- Start of picture text --> A. Level of capital stock relative to capital stock with 5% B. Growth rate of the capital stock with different<br>depreciation depreciation rates<br>16 3.0<br>1.00 14 Different growth rates 2.5<br>2.0<br>0.95 12<br>1.5<br>0.90 10 1.0<br>8 0.5<br>0.85<br>6 0.0<br>0.80 -0.5<br>4<br>0.75 2 spread in growth rates -1.0-1.5<br>0.70 0 -2.0<br>6% 7% 8% 9% 10% 5% 6% 7% 8% 9% 10%<br>1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015<br><!-- End of picture text --> _Source:_ Author estimates using data defined above 19