The Change to National Debt Thresholds Brought by Financial Crisis

Much of the modern theoretical discussion between debt and growth was initiated by Barro (1979). In this paper, Barro (1979) extends and analyzes the Ricardian Equivalence theorem. We first assume that the government increases government debt to stimulate the economy. The Ricardian Equivalence theorem states that consumers are forward-looking and realize that future taxes will have to rise to pay back the increase in government debt. Therefore, consumers will save any “extra income” (from the tax cut brought about by the government stimulus), keeping consumption (and total demand) constant (Barro, 1974)

From the Ricardian Equivalence theorem, we see that an increase in public debt doesn’t effect GDP. However, this theorem is based on strong assumptions- consumers are rational, all “extra income” will be saved”, future government actions are predictable, etc. In reality, these assumptions generally aren’t true. Elmendorf and Mankiw (1998) start their analysis by assuming that Ricardian Equivalence doesn’t hold. They assume that a budget deficit has been created by reducing taxes, keeping government spending constant. If taxes have been reduced households will have more disposable income. A portion of this income will be used to increase consumption.

An increase in consumption leads to an increase in GDP growth. Therefore a budget deficit leads to an increase in growth in the short-run (Elmendorf and Mankiw, 1998). In the long run, public savings reduces due to a fall in tax revenue. Most classical economists agree that private savings increases, but by less than what public savings decreases by (counter to Ricardian Equivalence). Total savings decreases meaning that total investment must also decrease. As investment is a component of AD, GDP will fall. Elmendorf and Mankiw (1998) quantify this reduction, finding that an additional dollar of debt leads to a 6 cents fall in GDP.

However, it’s fruitless to separate the relationship between debt and growth into two distinct periods. Short term events like a supply side-shock normally reverberate far into the future (Ball (2014) finds that the 2008 recessions caused a 8.4% decrease in predicted output in 23 OECD countries) Aschauer (2000) creates a theoretical model that analyzes the relationship between public debt and growth. The author does this by finding an optimal level of public to private capital (public borrowing equals the ratio of the two). He finds that growth is maximized when the post-tax marginal product of private capital equals the marginal product of public capital. A key assumption of Aschauer’s (2000) model is that there’s no technological growth, population growth, or depreciation. Checherita-Westphal et al. (2012) extend Auscher’s (2000) model by including population growth. They conclude that the steady-state level of debt (optimal debt level in the long run) is a function of the output elasticity of public debt. By using a theoretical model, their results can be extended to any country (or set of countries that displays the same set of characteristics).

One factor neglected by Aschauer (2000) and Checherita-Westphal et al. (2012) is the private savings rate. The savings rate has a direct relationship with both private and public capital (and therefore investment). If the above models included the savings rate, it can be speculated that the optimal debt GDP-level will be lower than the level suggested by Checherita-Westphal et al. (2012). Dombi and Dedák (2019) support this by finding that in a country with a high savings rate, a 90% debt threshold will reduce steady-state output by 9%. Furthermore, achieving the optimal level of debt in Checherita-Westphal et al. (2012)’s model requires knowing the output elasticity of public debt. This is very difficult to calculate this for a large economy and reaching the optimal level of debt may not be feasible. From the review above, most of the theoretical literature suggests a negative, non-linear relationship between debt and growth. The empirical literature below applies the theoretical models above to different data sets to try and quantify a relationship between debt and growth.

Empirical Issues

Endogeneity

Endogeneity occurs when any independent variable is correlated with the error term. It’s most often brought about by a measurement error in one of the independent variables or by completely omitting a relevant variable. When endogeneity is present, OLS estimates are biased and inconsistent. Reverse causality is a form of endogeneity and occurs when the dependent variable causes a change in the independent variable. Reverse causality is an important issue in the relationship between debt and growth. Theoretically, low levels of growth can lead to high levels of debt; during a recession, economies use government spending, funded by borrowing (increase in debt), to spur economic growth. Thus, low economic growth (recession) has led to a rise in debt (reverse causality). Endogeneity (and reverse causality) can be corrected by using instrumental variables, Generalized Methods of Moments (GMM), or lagged values for explanatory variables. The following section looks at how different papers account for endogeneity.

Solutions for Endogeneity

Cecchetti et al. (2011) use 5 year forward averages for all of their variables to try and mitigate endogeneity. They find that after controlling for credit flows and banking crisis, a 10% increase in the debt-GDP ratio causes economic growth to reduce by 0.17%, a highly negative effect. Cecchetti et al. (2011) recommend that governments immediately reduce debt levels to maintain strong growth. Panizza and Presbitero (2014) use the same set of countries and include the same explanatory variables as Cecchetti et al. (2011). However, they use instrumental variable regression as their primary form of estimation. Their contribution to the literature is using a completely new instrumental variable. Using OLS as a base model, Panizza and Presbitero (2014) find similar results to Cecchetti et al. (2011). After using a valuation effect (VE), “brought about by the interaction between foreign currency debt and movements in the exchange rate” (page 4) as an instrument for the debt-GDP ratio, the authors find no relationship between debt and growth.

One issue with the instrumental variable used by Panizza and Presbitero (2014) is that it equals zero for countries that have little to no foreign currency reserves (Table 1 [cite this better] ). Therefore, this instrumental variable excludes countries like the USA, Germany, France, Japan, and the Netherlands from the analysis. These countries are important to include as they are viewed as leaders in the financial world and analysis without them may be deemed incomplete. As Panizza and Presbitero (2014) and Cecchetti et al. (2011) analyzed the same countries and included the same explanatory variables, it is interesting to see their opposing results. The fact that both papers initially find similar results when using OLS but differ when Panizza and Presbitero (2014) uses 2SLS would suggest that endogeneity is present in the model and must be accounted for. However, the instrumental variable that Panizza and Presbitero (2014) used had no precedent in the literature and hasn’t been used in following papers. Although Panizza and Presbitero (2014) perform robustness checks, it would be interesting to see how results change when alternative estimation techniques are used (like GMM and SGMM)

Checherita-Westphal and Rother (2012) analyze 12 Euro countries from 1990-2010. They use two different instrumental variables for the debt ratio: the average government debt of the other 11 countries in the sample and lagged government debt. Checherita-Westphal and Rother (2012) find a negative non-linear relationship between debt and growth in the short-run. An important caveat to this result is that when Checherita-Westphal and Rother (2012) use the average government debt of the other 11 countries as their instrument, they’re assuming that one country’s debt level doesn’t affect another country’s GDP growth level (exogeneity condition) (Panizza and Presbitero, 2014). This may not be true (especially when considering Euro countries) as countries are interconnected and a shock to one country’s economy will reverberate through other countries economies. This is further relevant with the continued integration of economies.

Padoan et al. (2012) combine instrumental variables regression and Generalized Methods of Moments (GMM), using GMM-IV regression. They use 1, 3, and 5 year forward rates for all their explanatory variables to account for reverse causality. Lagged values of the sovereign debt ratio and the primary debt ratio are used as instruments for the respective debt-GDP ratio. Padoan et al. (2012) find that a 1 percentage point increase in public debt reduces GDP growth for the following five years by 0.02 percentage points (above some endogenously determined threshold). Kumar and Woo (2010) use a form of GMM, but state that it’s difficult to find suitable instrumental variables for the explanatory variables, thus preferring to use System Generalized Methods of Moments (SGMM). Kumar and Woo (2010) believe that SGMM is the best method of estimation as it can account for endogeneity, omitted-variable bias, and measurement errors. Using this method of estimation, Kumar and Woo (2010) find that a 10% increase in initial GDP leads to a 0.2% decrease in GDP growth per capita. This finding is similar to Cecchetti et al. (2012).

After accounting for endogeneity and reverse causality, the above papers (bar Panizza and Presbitero, 2014) find evidence for a negative relationship between debt and growth. These results provide econometric support for the theoretical arguments proposed by Elmendorf and Mankiw (1998), Aschauer (2000), and Checherita-Westphal et al. (2012).

Measurement Error

Measurement errors in the data is also an issue. Finding a relationship between debt and growth depends on having good quality data. This isn’t a problem for papers that use data from the modern era as common data sources (World Bank, IMF, OECD, etc.) have rigorous data collection methods. However, Égert (2013), RR(2010), Pescatori et al. (2014) and Herndon et al. (2013) analyze over 200 years of data. Due to accounting errors, different ways of calculating values and lost records, data before the 19th century may not be as reliable. Furthermore, there are “gaps in the data” (e.g RR(2010) missing data from Australia, New Zealand, and Canada (Herndon et al. 2013) which skew results. To solve this, papers can perform robustness tests by using data from different sources. Instrumental variables can also be used if data for an independent variable is hard to find.

Calculating a uniform debt-GDP threshold that countries can aim towards is the “golden egg” of this topic. If there is a magical debt threshold, after which an increase in debt leads to a decrease in GDP growth rates, countries can aim to have their debt-GDP ratio at this level, thus never having to worry about reducing growth. Perhaps the most important paper written about the relationship between debt and growth is Reinhart and Rogoff’s (RR hereafter) 2010 Paper “Growth in a Time of Debt”. RR (2010) created 4 groups of countries- those with a debt-GDP ratio of below 30%, a ratio between 30 and 60%, a ratio between 60 and 90% and a ratio above 90%. Their findings showed that average GDP growth rates were 4% lower and median growth rates were 1% lower for advanced economies above a 90% threshold. The fact that average GDP growth fell by a lot more than median GDP growth would suggest the presence of outliers (median is immune from outlier effects). The outliers should have been accounted for, by either removing them or reducing their weighting. The presence of unaccounted outliers would suggest a heavy skew in the data. There is a subset of papers that extensively critique RR (2010) findings. Chief amongst this is Herndon et al. (2013). They analyze RR (2010) dataset and find extensive issues with the data. The main issues found are that RR (2010) excludes data from different countries and years, a coding error is present in the spreadsheet used, and an unconventional method of weighting is used to calculate average GDP growth. The problems are exacerbated in the “Above 90% threshold” grouping, where a few countries heavily skew the data. Similar critiques of RR (2010) can be found in Irons and Bivens (2010).

Even with the problems found by Herndon et al. (2013), several papers that support the 90% threshold. Using 18 OECD countries with data from 1980-2010, Cecchetti et al. (2011) initially find a debt threshold of 85% of GDP. After accounting for crises, the debt threshold jumps to 96% of GDP. Similarly, using 12 Euro countries, Checherita- Westphal and Rother (2012) find that there’s a maximum debt-GDP ratio (some value x) between 90% and 100%. The maximum would suggest a positive relationship between debt and growth before x and a negative relationship after x. Baum et al (2012) extends Checherita-Westphal and Rother (2012) model to endogenously identify a threshold. Using data from 1990-2010,. Baum et al. (2012) finds two thresholds. One threshold is at 66.4% (below this threshold, debt and growth have a positive relationship) and the other threshold is at 95.6% (above this threshold, debt has a negative effect on growth). Between the two periods debt has no effect on growth.

The three papers above come to very similar results. This is because they all looked at very similar countries (there a were a number of overlaps in the 18 OECD countries used by Cecchetti et al. (2011), and the 12 Euro countries used by Checherita-Westphal and Rother (2012)). Furthermore, the papers used comparable models (similar explanatory variables) and the same threshold estimation technique (either Panel Threshold Regression (PTR) or Dynamic Panel Threshold Regression). The commonality in the regression technique and data set means that it’s unsurprising these papers reached similar conclusions.

One paper that stands out is Minea and Parent (2012). The authors use Panel Smooth Threshold Regression (PSTR) to estimate the relationship. This allows for a steady, continuous change in the regression coefficient rather than sudden changes at some threshold value (Minea and Parent, 2012). Minea and Parent (2012) find that advanced economies experience a fall in GDP growth above a 90% threshold. However, above a 115% threshold, the relationship between debt and growth becomes positive again. While this implies that countries that reach the 90% threshold should keep increasing debt until it reaches the 115% level, Minea and Parent (2012) caution against this.

One major reason that Minea and Parent (2012) differs from the other papers in this section is due to the data set they use. Their paper includes data from 1800-2008. This adds about 200 more years of data, compared to data sets used by Checherita-Westphal and Rother (2012) and Cecchetti et al. (2011). The additional data has numerous years with both high debt levels and high economic growth (during times of war), which skew the results.

There are a few papers that support a threshold, but find one that is significantly below 90%. Égert (2013) extends RR(2010) paper by including data from 1790 onwards, adding 90 years of data. Égert (2013) finds that endogenously determined thresholds occur at very low levels (the first threshold is around 30% of GDP and the second is around 60% of GDP in advanced economies). Herndon et al. (2013) echo Égert (2012) by finding a threshold at 30%, after correcting the errors present in RR(2010) data set. While the presence of a threshold suggests that economies should aim for this value, many economists caution against it. Cecchetti et al. (2011) suggest that countries should target a debt-GDP level that is below the threshold. This creates a buffer, allowing countries to increase their debt levels to prompt economic growth if needed.

Against Threshold

Chudik et al. (2015) state that previous papers like Checherita-Westphal and Rother (2012) and RR(2010) fail to take cross-sectional dependence between countries into account. The authors analyze 40 countries from 1965-2010. Using CS-ARDL and CS-DL estimation techniques (which account for endogeneity, heterogeneity, and cross-sectional dependence (Chudik et al. 2015)), no universally applicable threshold is found. Pescatori et al (2014) come to a similar conclusion when analyzing 19 advanced economies over 200 years. After factoring for reverse causality, there’s no evidence of a threshold in the long-run relationship between debt and growth. Pescatori et al (2014) however, state that debt trajectory is more important than debt values, and countries should nonetheless try and find ways to reduce debt levels.

Schclarek (2004) estimates a non-linear relationship between debt and growth using spline regression. The author combines this with SGMM (similar to Kumar and Woo (2010)) to combat endogeneity and reverse causality. Analyzing 24 industrial countries (very similar to advanced economies), Schclarek (2004) finds no evidence of a U-shaped relationship (and thus no evidence for a threshold) between debt and growth. Interestingly, the results showed a positive relationship. Panizza and Presbitero (2014) also found a positive relationship between debt and growth.

The difference between papers that support a threshold and those that contradict a threshold lies in the data set. Those that support a threshold have focused data sets, containing a small set of countries over a relatively small period (Checherita-Westphal and Rother (2012)). This allows for more concentrated analysis as the results can be applied to countries that exhibit similar characteristics. It’s also easier to account for cross-country differences because the countries all display similar characteristics. Those that contradict thresholds use data from a large spread of countries over a long period (e.g. Pescatori et al (2014)). Using a large number of countries over a long period exacerbates endogeneity, heterogeneity, causality, and cross-country differences. It’s difficult to accurately control for all of these when considering a large data set. Furthermore, the world economy has changed over the past 300 years. Conclusions from 19th-century data may not be applicable anymore.