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Lower-than-expected growth can derail fiscal consolidations.²¹ Conversely, concern is also often expressed that the impact of fiscal expansion on output is underestimated. It is therefore critical to have a realistic picture of the impact of fiscal consolidation and expansion on growth and debt dynamics. This tool compares the baseline growth projection against growth paths that assume only a fiscal impact from the last observed growth rate, with the fiscal impact calculated under a range of plausible fiscal multipliers, using a default persistence parameter of 0.6.

This tool displays the range of possible projected growth paths consistent with different fiscal multipliers. Given the country team鈥檚 assumed fiscal multiplier, the tool calculates the underlying projected growth rates (i.e. the counterfactual that would materialize absent fiscal adjustment). For any projected growth and fiscal adjustment paths under the baseline scenario, the underlying projected growth path can be computed as follows:

Underlying projected growth =

Projected growth (including fiscal adjustment) + change in growth due to fiscal adjustment

The change in growth due to fiscal adjustment depends on the size and persistence of the assumed fiscal multiplier. The tool assumes an AR(1) process to model the evolution of the fiscal multiplier:

饾憵^饾憽 = 饾憵 鈭� 饾憹 ^{饾憽鈭�1}

where 饾憵 is the size of the impact multiplier, defined as the percent change of real GDP from a one percentage point adjustment in the structural primary balance (as percent of GDP) during the first year of full impact. Given that the effect on growth of fiscal adjustment can take time to be fully realized, the first year of full impact is set as the year after the implementation. The impact during the implementation year itself is assumed to be half of the impact multiplier. The persistence of the multiplier is captured by 饾憹, the autocorrelation coefficient (default value is set at 0.6).

To get more information please check out the LIC DSF Policy here.

The growth accounting methodology is based on a standard functional form assumption for the aggregate production function. Specifically, the aggregate production function is assumed to be isoelastic in government capital:

饾憣_饾憽 = 饾惡_饾憽^饾浗饾惞(饾惔_饾憽,饾惥_饾憽,饾惢_饾憽)

where 饾憣_饾憽 is real GDP; 饾惡_饾憽 is government capital; 饾浗 is the output elasticity of government capital, and 饾惞(饾惔_饾憽 ,饾惥_饾憽,饾惢_饾憽) is a function of productivity (饾惔_饾憽), private capital (饾惥_饾憽), and human capital (饾惢_饾憽) that does not need to be fully specified. Given this functional form, there is a simple decomposition of output growth:

where the first term represents the contribution of changes in government capital to growth, and the second term _饾渶饾憽 represents the contribution of all other factors and productivity to growth. This decomposition captures only the direct effects of changes in government capital on growth, and does not consider possible endogenous responses of productivity or private factors of production to increases in government capital. Country teams interested in pursuing these richer channels can do so with the help of more sophisticated models such as those referenced above. Based on existing literature, this tool sets the output elasticity of government capital at 饾浗 = 0.15.¹

The growth rate of the government capital stock can be inferred from the path of public investment, together with assumptions on an initial stock of government capital, depreciation rates, and public investment efficiency. The accumulation equation for government capital is:

where 饾浛 is the depreciation rate (set at 0.05), 饾湙_饾惞 is the public investment efficiency (that can be calibrated using FAD鈥檚 estimates), and 饾憱_饾恶饾憽 is the public investment path. This equation is used to project the path of the government capital stock, from which growth rates of the government capital stock can be calculated.

The analysis can accommodate assumptions about the 鈥渆fficiency鈥� of past and future government investment. In this context, 鈥渆fficiency鈥� refers to the fraction of a dollar of government investment that turns into government capital. Incorporating efficiency involves (i) replacing the projected future investment rate with 饾湙_饾惞饾憱_饾恶饾憽, and (ii) scaling down the historical capital stock series by a factor 饾湙_饾惢. The efficiency parameters 0 < 饾湙_饾惞 鈮� 1 and 0 < 饾湙_饾惢 鈮� 1 reflect judgement as to the efficiency of future and past investment. The adjustment for historical efficiency is important: if past efficiency of public investment was low, then the accumulated investment flows on which the historical capital stock series are based are an over-estimate of the actual stock of government capital, and the marginal productivity of an additional dollar of government investment is underestimated (see Berg and others (2015)). ²While DSF users can separately specify the historical and future efficiency parameters, the analysis in the realism tool depends only on the ratio of the two, 饾湙饾惞/饾湙饾惢. The benchmark assumption is that 饾湙_饾惞 = 饾湙_饾惢 = 1 and departures from the benchmark, particularly those that imply an improvement in efficiency, would require careful justification by country teams.

To get more information please check out the LIC DSF Policy here.