Keywords: Government debt, GDP growth, fixed effects estimator, recursive demeaning, near unit-root process, threshold, subsampling.
This paper explores the empirical relationship between government debt and future macroeconomic activity using data on twenty advanced economies throughout the post-war era. We use robust inference techniques to deal with the bias arising from the persistent nature of debt to GDP ratio as an endogenous predictor of GDP growth. Our results show that statistical significance of the csoefficient on the debt ratio in predictive regressions changes considerably with the use of robust inference techniques. For countries with relatively low average debt ratios we find a negative threshold effect as their debt ratios increase toward moderate levels. For countries with chronically high debt ratios, GDP growth slows as relative government debt increases, but we find no significant threshold effect.
In the aftermath of the recent global financial crisis, government debt in most advanced economies surged due to high levels of stimulus spending and costs of stabilizing the financial system. Aging populations and the associated social insurance costs create further pressure on public debt levels relative to total income in these economies, e.g. (Cecchetti et al., 2010).
Public debt can facilitate intergenerational transfers that allow consumption smoothing, e.g. (Cukierman & Meltzer, 1989), or provide liquidity services that can ease credit conditions for private agents, e.g. (Woodford, 1990). However, higher public debt may result in weaker economic performance due to crowding out, limitations on government services, and lower investment and hiring through real option effects due to increased uncertainty associated with high debt levels, e.g. (Baker et al., 2012).3 Moreover, as argued by (Cecchetti et al., 2011), we do not have a fully satisfactory theoretical framework to quantitatively evaluate effects of public debt accumulation, so empirical evidence is crucial to guide policy makers.
There is a growing empirical literature that evaluates effects of government debt on economic activity. (Reinhart & Rogoff, 2010) construct a historical multi-country data set and provide a comprehensive descriptive analysis of debt-growth and debt-inflation relationships. They find that a debt to GDP ratio higher than 90% is associated with considerably lower average real GDP growth rates. (Reinhart et al., 2012) identify episodes of public debt overhang in advanced economies and discuss the subsequent growth experience in detail. (Cecchetti et al., 2011), (Cecherita & Rother, 2010), and (Kumar & Woo, 2010) investigate the relationship between government debt and real activity by estimating growth regressions. These studies provide mixed evidence regarding the direction and significance of the relationship and potential nonlinearities.
We contribute to the empirical literature on the relationship between government debt and economic activity by putting the (Reinhart & Rogoff, 2010) data set for the post-war period in a formal statistical context. We aim to determine whether a higher level of debt to GDP ratio predicts slower GDP growth in the medium term, as opposed to investigating the steady state relationship between growth in per capita income and public debt, which is the focus of the aforementioned studies. Endogeneity and high persistence of debt to GDP ratio causes finite sample bias in a standard panel data setting, which we deal with using robust statistical inference techniques. We also investigate the possibility that there is a certain tipping point for debt to GDP above which further debt accumulation starts to have negative effects on output growth or already negative effects are amplified. We use subsampling methods for inference in the context of a tipping point as standard inference techniques are not applicable due to the presence of nuisance parameters under the null of a linear relationship.
Our findings can be summarized as follows. In a linear framework, higher government debt relative to GDP is not a statistically significant predictor of subsequent GDP growth when all 20 advanced economies are considered together. There is an economically significant negative threshold effect when debt to GDP ratio is close to 20%, but the threshold estimate is subject to considerable uncertainty. Data indicates considerable heterogeneity with respect to average debt ratios, so we split countries into two groups accordingly. We find that the aforementioned threshold effect is mainly driven by the countries that experienced relatively low average debt to GDP levels over the sample period. Moreover, there is a significant negative linear predictive relationship between debt to GDP and GDP growth for countries with chronivally high debt to GDP ratios but we do not find evidence for a debt tipping point for such countries.
The rest of the paper is organized as follows. We provide a detailed discussion of methodological issues in Section 2. We present and discuss the empirical results in Section 3 and conclude in Section 4.
Let and denote GDP growth and debt to GDP ratio respectively for the th country in the sample for , and . We are interested in the following simple predictive regression4
The standard fixed effects (FE) estimator in this framework is given by
Recursive demeaning has been proposed in the literature as a solution to the aforementioned finite sample bias in a panel data setting (see (Phillips & Moon, 2000)). Following (Hjalmarsson, 2010) we assume that
The second approach that we consider to deal with the finite sample bias arising due to persistent endogenous predictors is subsampling, e.g. (Wolf, 2000). This approach also allows us to investigate the possibility of a tipping point in government debt and make simultaneous inference about the predictive coefficients as well as the debt to GDP threshold. Subsampling is valid under both the local to unity structure described above in case of the RD estimator and fixed roots close to unity. To illustrate the subsampling procedure, let us consider the following nonlinear version of the model
Under the null of linearity (i.e. ), is not identified, so standard inference methods are not applicable but subsampling is valid under relatively mild assumptions, e.g. (Gonzalo & Wolf, 2005). Subsampling is based on the idea of estimating the model on moving blocks, or subsamples, of the original data and using the resulting empirical distribution to approximate the unknown distribution of interest. Let denote the block size, such that and let denote the threshold estimate on the block for . Define where is the full sample estimate, i.e. , and is the probability law governing . The subsampling approximation to is defined as follows
We use the post-war portion of the historical multi-country data set of (Reinhart & Rogoff, 2010) as our methods require a balanced panel and previous periods have numerous missing observations.8 Specifically, our annual sample runs from 1954 to 2008. The countries included in the data set are: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, United Kingdom, and United States.
Table 1 provides summary statistics for GDP growth. The average annual GDP growth across countries is about 3.4% over the sample period. On average, GDP growth is slightly persistent and has an approximately symmetric distribution. Table 2 summarizes basic characteristics of debt to GDP ratio.9 Average debt to GDP across countries and over time is about 44%. The distribution of debt to GDP is right skewed for most countries in the sample. Unit root test results reflect high persistence in debt to GDP ratios. Only for two countries, Denmark and Sweden, the null of unit root can be rejected at conventional levels according to the point optimal test statistic of (Elliott et al., 1996). Debt to GDP ratios for individual countries are shown in Figures 1-2.
Table 3 summarizes results for the linear model for three, five, and ten-year horizons. We present three types of symmetric confidence intervals for the predictive coefficient: asymptotic FE, asymptotic RD, and subsampled FE. We use heteroskedasticity and autocorrelation consistent covariance standard errors for the asymptotic methods and set confidence level to 90% in all cases. The conventional method (asymptotic FE) implies a significant negative predictive relationship between debt to GDP and GDP growth. However, the two alternative procedures have quite different implications. Under the RD scheme, the point estimates become much larger in absolute value, sometimes implausibly so. The predictive coefficient is also always insignificant under this scheme. These results suggest presence of finite sample bias in the standard FE estimator and the bias-variance trade-off inherent in the RD estimator, so we conjecture that subsampled FE strikes a reasonable balance between bias and variance. The subsampled FE confidence intervals suggest no significant predictive relationship, but the width of the intervals are much smaller compared to the case of RD procedure but wider than the asymptotic FE, and on average, a notable portion of the intervals are on the negative part of the real line. The fifth percentile estimates suggest a 0.5-1.64% drag on annual GDP growth for a 10 percentage point increase in the debt to GDP ratio.
There appears to be an insignificant relationship between GDP growth and debt ratio in a linear predictive context, so we proceed to the nonlinear case to uncover the potential effects of debt intolerance at higher levels of government debt. For threshold estimation, we consider a symmetric trimming scheme that drops 15% of observations from each side of the sample distribution of debt to GDP ratios to form the search grid.10 Results are presented in Panel A of Table 4. For the three and five year horizons, point estimates of the threshold are relatively low, close to 18% while the estimate for the 10-year horizon is about 58%. In all cases, there is considerable uncertainty surrounding the point estimate of the threshold according to the subsampling confidence intervals. Interestingly , debt to GDP has a positive and significant coefficient below the threshold while it is not statistically different from zero above the threshold for three and five year horizons. Our interval estimates for the three and five year horizons imply that the expected growth differential between the two states can be as large as 3.7% per year. These estimates suggest that potential growth enhancing effects of public debt accumulation disappear at relatively low levels.
The estimated thresholds are low and the confidence intervals are fairly wide for the threshold in cases where predictive coefficients are significantly different across regimes, so we also consider a more restricted grid search to estimate the potential threshold at higher values of the debt ratio. Specifically, we extend the trimming from the left by dropping all the observations below the median and keep trimming at 15% on the right. Under this restricted scheme we find that the estimated threshold is, on average, close to 53% across all horizons considered (Table 4, Panel B). The predictive coefficient of debt to GDP is significantly negative only above the threshold for the three year horizon and both above and below the threshold for the five year horizon. However, in both cases the threshold effect is not significantly different from zero as indicated by the subsampling confidence intervals. To sum up, existence of a common debt threshold that is statistically and economically significant does not seem to be an accurate description of the nonlinear dynamics in the data when we consider all the countries jointly.
Our results so far suggest that there may be too much heterogeneity with respect to debt to GDP levels and dynamics to consider all countries jointly. For example, for seven countries in the sample debt to GDP ratio was never below 18%, the estimated threshold for three and five year horizons. Hence, we split the countries into two groups with respect to their average debt to GDP ratios over the sample and perform estimation for the low-debt and high-debt countries separately. This yields Australia, Austria, Denmark, Finland, France, Germany, Norway, Portugal, Spain, and Sweden as the low-debt group while the high-debt group is comprised of Belgium, Canada, Greece, Japan, Ireland, Italy, New Zealand, UK, and US.11
Results for the linear case are presented in Table 5. The conventional interval estimates based on the FE estimator suggest significance in case of both country groups but subsampling confidence intervals indicate that debt to GDP predicts a significantly slower growth rate for high average debt countries for up to five years and the predictive coefficient is nearly significant at the 10-year horizon. For the nonlinear case we report results under symmetric trimming for both country groups in Table 6. For the three year horizon, the predictive coefficient is positive and significant below the estimated threshold of 18% and there is a significant negative threshold effect. For five and 10 year horizons, estimated thresholds are close to 30% and the predictive coefficients are not distinguishable from zero. However, a much bigger portion of the subsampling intervals lie in the positive (negative) region for ( . So the threshold effect is in the expected direction but it is subject to large uncertainty for five-year and ten-year horizons. For high-debt countries, the estimated thresholds average out to about 50% across the three horizons. The predictive coefficient tends to be negative both above and below the threshold and the difference between the two regimes is not statistically distinguishable from zero. These results reinforce our previous finding that a higher debt to GDP ratio predicts a slower growth rate for high average debt countries in a linear fashion. Our subsampling based confidence intervals imply that for a 10 percentage point increase in the debt to GDP ratio, annual output growth slows between 2 and 48 basis points per year for the high average debt group.
This paper contributes to the growing empirical literature on exploring implications of higher levels of government debt relative to total output for macroeconomic activity. We put the post-war portion of the (Reinhart & Rogoff, 2010) data set in a formal statistical context using estimation and inference techniques suitable to the underlying data characteristics. We find that endogeneity and persistence of government debt relative to total output causes considerable finite sample bias in a standard predictive panel data setting. We use robust inference techniques to deal with this problem. We find that higher debt relative to GDP is not a statistically significant predictor of subsequent economic growth in a linear framework. We also do not find evidence for a common debt to GDP threshold that is economically and statistically significant. However, when we split countries into two groups with respect to their average debt ratios, we find that there is a negative threshold effect for the low average debt countries and a significant negative linear predictive relationship for countries that experienced relatively higher levels of debt. We do not find evidence for increasing debt intolerance at higher levels of debt to GDP.
Tables and Figures
Notes: This table reports mean, 10th, 50th and 90th percentiles, and the first order autocorrelation coefficient (ACR) for GDP growth. Annual sample runs from 1954 to 2008.
Indicates significance at 10% level.
Indicates significance at 5% level.
Indicates significance at 1% level.
|Country||Mean||Std. Dev.||10th||50th||90th||UR Test|
Notes: This table reports mean, 10th, 50th, and 90th percentiles, and the point optimal unit root test statistic of (Elliott et al., 1996) (UR Test) for debt to GDP ratios. Annual sample runs from 1954 to 2008.
Indicates significance at 10% level.
Indicates significance at 5% level.
Indicates significance at 1% level.
|[ -0.0361 -0.0113]||[ -2.3793 1.6179]||[ -0.0492 0.0021]|
|[ -0.0357 -0.0103]||[ -1.0554 0.5214]||[ -0.0815 0.0030]|
|[ -0.0300 -0.0060]||[ -0.2319 0.0159]||[ -0.1640 0.0070]|
Notes: This table reports 90% symmetric confidence intervals for the predictive coefficient of debt to GDP ratio in the linear model (see Equation 1). ACI stands for asymptotic confidence interval; SCI stands for subsampling confidence interval; FE stands for fixed effects; and RD stands for recursive demeaning. Annual sample runs from 1954 to 2008. See Table 1 for a list of countries in the sample.
|Panel A: Symmetric trimming||18.33||[8.58 28.09]||[0.0282 0.1170]||[-0.0387 0.0072]||[-0.1215 -0.0555]|
|Panel A: Symmetric trimming||18.80||[0.65 36.95]||[0.0215 0.1155]||[-0.0425 0.0130]||[-0.1325 -0.0340]|
|Panel A: Symmetric trimming||58.40||[41.17 75.63]||[-0.0970 0.0260]||[-0.0530 0.0120]||[-0.0470 0.0780]|
|Panel B: Asymmetric trimming||57.33||[53.36 61.31]||[-0.0849 0.0033]||[-0.0492 -0.0042]||[-0.0138 0.0414]|
|Panel B: Asymmetric trimming||46.60||[35.91 57.29]||[-0.0925 -0.0050]||[-0.0570 -0.0005]||[-0.0015 0.0415]|
|Panel B: Asymmetric trimming||58.40||[51.14 65.66]||[-0.0980 0.0260]||[-0.0630 0.0220]||[-0.0330 0.0630]|
Notes: This table reports threshold estimates and 90% subsampling confidence intervals for the thresholds and predictive coefficients in the nonlinear model (see Equation 5). Symmetric trimming corresponds to the case where 15% of observations are trimmed on each side of the sample observations on debt to GDP while 50% is trimmed from the left and 15% from the right in case of asymmetric trimming. Annual sample runs from 1954 to 2008. See Table 1 for a list of countries in the sample.
|Panel A: Low-debt Countries||[ -0.0338 -0.0022]||[ -1.0652 0.4550]||[ -0.0789 0.0432]|
|Panel A: Low-debt Countries||[ -0.0329 -0.0041]||[ -0.6060 0.1530]||[ -0.0770 0.0400]|
|Panel A: Low-debt Countries||[ -0.0262 -0.0018]||[ -0.2220 -0.0040]||[ -0.0920 0.0630]|
|Panel B: High-debt Countries||[ -0.0411 -0.0105]||[ -6.1771 5.2153]||[ -0.0462 -0.0054]|
|Panel B: High-debt Countries||[ -0.0414 -0.0086]||[ -1.9693 1.3613]||[ -0.0475 -0.0025]|
|Panel B: High-debt Countries||[ -0.0364 -0.0036]||[ -0.2859 0.0779]||[ -0.0510 0.0120]|
Notes: This table reports 90% confidence intervals for the predictive coefficient of debt to GDP ratio in the linear model (see Equation 1). ACI stands for asymptotic confidence interval; SCI stands for subsampling confidence interval; FE stands for fixed effect; and RD stands for recursive demeaning. Annual sample runs from 1954 to 2008. Low-debt countries include Germany, Finland, Norway, Portugal, Australia, Spain, Austria, France, Denmark, and Sweden. High-debt countries include New Zealand, Japan, US, Greece, Canada, UK, Netherlands, Ireland, Italy, and Belgium.
|Panel A: Low-debt Countries||18.00||[10.32 25.68]||[0.0312 0.1647]||[-0.0417 0.0462]||[-0.1641 -0.0273]|
|Panel A: Low-debt Countries||31.80||[26.89 36.71]||[-0.0325 0.1335]||[-0.0440 0.0390]||[-0.1220 0.0160]|
|Panel A: Low-debt Countries||28.40||[22.37 34.43]||[-0.0880 0.1430]||[-0.0860 0.0790]||[-0.1260 0.0630]|
|Panel B: High-debt Countries||46.00||[38.27 53.73]||[-0.1170 -0.0168]||[-0.0594 -0.0132]||[-0.0162 0.0774]|
|Panel B: High-debt Countries||46.40||[33.75 59.05]||[-0.1630 0.0165]||[-0.0680 -0.0075]||[-0.0770 0.1480]|
|Panel B: High-debt Countries||58.40||[47.77 69.03]||[-0.1470 0.0270]||[-0.0720 0.0070]||[-0.0510 0.1060]|
Notes: This table reports threshold estimates and 90% subsampling confidence intervals for the thresholds and predictive coefficients in the nonlinear model (see Equation 5). For estimation of the threshold, a symmetric trimming scheme is considered where 15% of observations are trimmed on each side of the sample observations on debt to GDP. Annual sample runs from 1954 to 2008. See Table 5 for a list of countries in each group.