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Online Appendix

This appendix describes the regression model discussed in "Size and structure of disaster relief when state capacity is limited: China's 1823 flood" which is currently under revision at the Australian Economic History Review.

The model estimated is:

 yi = c + b1*x1i + b2*x2i + b3*x3i + b4*x4i + b5*x5i + ui


yi = [Land Tax Relief Ratio, Relative Land Tax Relief Ratio]

x1i = [Disaster Ratio, Wetness Index, Disaster Ratio*Pop, Wetness Index*Pop]

x2i = Population density

x3i = Land Tax Quota

x4i = Grain Stored Per Capita Change Between 1786 and 1820

x5i = Distance to Beijing

ui = i.i.d. normally distributed error term

The coefficients were estimated with OLS.

For models with the Land Tax Relief Ratio, an alternative specification was estimated that corrects for the truncation of the dependent variable. The results were, however, almost the same, as shown in estimations 5, 6, 11 and 12.


Dependent variables

(1)  Land Tax Relief Ratio (LandTaxRel~o): this is the reduction from the land tax expressed as a percentage of the long-term quota. The higher this number, the higher the relief.

(2)  Relative Land Tax Relief Ratio (RelativeLa~o): this is the change in the reduction of the land tax’s long-term quota and accounts for the fact that the long-term quota was often reduced quasi-permanently and thus not likely to depend on yearly variations in the conditions. To allow for the same interpretation as for variable (1) it has been multiplied by -1 in the regressions.


Independent variables of interest

(1)  Disaster Ratio (Disasterra~o): the number of counties reporting flooding as a share of all counties in a province. The higher this number, the higher the exposure to the flood.

(2)  Wetness Index (Wet_Map_1823): an index constructed from contemporary sources measuring precipitation on a scale from 1 = wet through to 3 = normal and 5 = dry. Thus, the lower this number, the higher the exposure to the flood.

(3)  Disaster Ratio Population Weighted (dispop): Disaster Ratio times the population in 1820.

(4)  Wetness Index Population Weighted (wetpop): Wetness Index times the population in 1820.


Further control variables

(1)  Population density (pop_dens): population in 1820 divided by area in square kilometres. The map shows that regions with high disaster exposure were in the areas of the Yangtze delta and North China plain, traditionally intensive agricultural regions and thus high population density and high-income regions. Central government disaster relief might have been influenced by this; for example, by directing funds to regions with higher economic potential and thus more political influence at the court. If this is true, the coefficient should be positive when regressing on Disaster Ratio and negative when regressing on the Wetness Index.

(2)  Land Tax Quota (land_tax_q~o): this is the long-term quota of land taxes in shi of rice. It was originally stipulated in the early eighteenth century and may be a reflection of agricultural productivity and its size. One might expect that regions with higher agricultural production might be hit harder by floods, and thus expect higher relief, or that simply higher quotas might profit from those quasi-permanent reductions of the quotas, for example, on account of political interventions. In any case, the coefficient is expected to be positive.

(3)  Grain Stored Per Capita Change Between 1786 and 1820 (grain~o_1786): this variable includes grain stored in civilian granaries in 1786 and 1820 divided by population, each measured as a change in time. It might be expected that provinces that saw a long-term reduction in the per capita amount of grain stored would either profit from more direct relief in the case of a flood or because of its degrading disaster relief precautions receive less relief from the capital. Thus, the coefficient might turn negative or positive.

(4)  Distance to Beijing (distance_b~g): this is the linear distance between Beijing and the provincial capitals. It accounts for the fact that regions closer to the capital enjoyed easier access to the court and thus might have received more relief. The coefficient should therefore be negative.



We report the regression results in 12 tables: Models 1-6 for simple disaster indicators and Models 7-12 for population weighted indicators. Each runs the relevant explanatory variable against one of the four controls and all of them at once. Of course, the number of observations with up to five independent variables plus a constant leaves very few degrees of freedom. However, leaving the constants out does not make a substantial difference, and the results are not shown for the sake of brevity, but can be requested from the authors.

Generally, when letting either explanatory variable in each of the eight models compete against only one of the controls the coefficient b1 survives in sign, size and significance. This means that the controls – although meaningfully chosen and correlated with the dependent variable – do not challenge the hypothesis that there is a proportional relationship between disaster impact and relief.

An exception is model (3), when the Land Tax Relief Ratio is regressed against the Wetness Index. This is a very weak model mainly for two reasons. Firstly, the Land Tax Relief Ratio is unlikely to be particularly well explained by the weather events of 1823, since it rather reflects quasi-permanent reductions of the land tax stipulated much earlier. Secondly, the Wetness Index is measured with a lot of error as the values were taken from a map and aggregated to provincial level according to their location on the map. This unsystematic error increases the standard errors and biases the results against our hypothesis. Thus, only without controls is there a correct sign and a t-statistic close to statistical significance. It is noteworthy that, as expected, provinces with higher quotas enjoyed permanently higher reductions in land tax (Column 3), and that provinces further away from Beijing enjoyed less permanent reductions (Column 5).

Our favoured model is 4. The dependent variable (Relative Land Tax Relief Ratio) reflects the change in the permanently lowered reduction in the given year, and is thus likely to be a reaction to events in this period. (Similar comments can be made about Model 2.)

One notable result in Models 1 and 3 is that provinces that improved their per capita holdings of grain in civilian granaries between 1786 and 1820 received larger permanent reductions in land tax before and during the 1823 flood but that there was no such relation to short-term reduction between 1822 and 1823 (Models 2 and 4).

Models 7-10 include the population weighted disaster indicators. The four provinces with the largest populations in 1820 were Jiangsu, Shandong, Anhui and Henan, all in the east, close to the capital and largely affected by the disaster. Thus, these indicators are likely to be correlated even more strongly with the dependent variables but also to be affected more strongly by controls such as population density, distance to Beijing and land tax quota. These predictions are neither strongly refuted nor underlined by the results (Models 7 and 8). What strikes the eye, though, is that the population weighted wetness index fails as an indicator of disaster intensity, while disaster ratio times population reproduces the results of the simple disaster indicators. What might drive this is that measurement error for eastern provinces is larger than in the west, because the provincial borders are more difficult to see with the naked eye, and this is then overweighted relative to the simple indicator because of the larger population in the east.

To conclude, the overall outcome of this exercise is that the hypothesis of a proportional relationship between disaster impact and relief from the central government can be substantiated quantitatively even when controlling for variables such as population density, permanent land tax quota, the changing state of the granary system, and distance to Beijing.