The effect of public debt on economic growth: an empirical
investigation across US states
Pim Dibbets (11666633)
Bachelor’s Thesis and Thesis Seminar Economics June 28, 2020
Statement of Originality
This document is written by Student Pim Dibbets, who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This study investigates what the effect is of public debt on economic growth, and is carried out using a sample of all states in the US from 1960 to 2018. In the fixed-effect models, a positive effect of public debt on economic growth is found, for both low and high debt categories. The effect is even stronger for high debt level categories: implying an increasing relationship and increasing marginal returns of debt. This result contrasts most prior cross-country research, that usually finds a negative marginal effect of debt for high debt levels. The found results are robust for any model specification when a long time span is used (1960 – 2017). However, when a short time span model is used (2010 – 2017) and more control variables are included, the results become insignificant.
Introduction
In recent years, public debt levels have accumulated rapidly across nations. This was most visible in 2008 when the world was stuck in a financial crisis, where public debt levels became so high that some governments were on the edge of going bankrupt (Greece, as the most extreme example). Public debt is sometimes necessary to boost economic activity, but (in the worst-case scenario) could lead to a whole country filing for bankruptcy. This would be the case if a country keeps on increasing debt, until a point where it becomes
unsustainable. It is clear that debt can be either good or bad, which will be further dived into in this study.
Similarly to other developed nations, the US, which is historically characterized as a country with a high debt level, saw a steep increase in public debt in recent decades, and even more after the financial crisis of 2008 (see Figure 1). The rising debt levels are generally not tackled or recognized by politicians; fiscal consolidation, it seems, is not a popular topic on the political agenda.
Figure 1: the US public debt as a fraction of GDP from 1966 to 2019
Source: FRED Economic Data
Note: shaded areas indicate recessions
In contrast with countries, which are able to file bankruptcy when they are in financial distress, individual states (in the US) are not able to do so. Even though some states are building up debt levels quickly, laws are in place that do not allow states to file for
bankruptcy. In 2017, these states include Kentucky (22.3 percent of GDP), New York (21.83 percent of GDP), Rhode Island (19.85 percent of GDP) and Illinois (18.74 percent of GDP). These numbers include both state and local government debt. Although these debt levels may not seem that high when compared to the national US debt level (which has surpassed 100 percent of GDP since around 2012), they are sufficiently high enough for politicians to start a discussion on whether states should be able to file bankruptcy again (which will be elaborated on later).
In Figure 2, the debt levels per capita are compared across different states. One could observe from the graph that New York has the highest debt per capita level, and
Figure 2: state and local debt per capita for US states in 2012
Source: US Census Bureau, State and Local Government Finances Note: the darker the state is marked, the higher the public debt
An important question in fiscal policy discussions is whether high public debt levels are actually damaging for the economy, or, more extremely, why high debt levels are even a problem at all. This question is especially important when fiscal consolidation policies are potentially implemented. Increasing public debt levels imply that states are paying a higher interest expense on their debt. In addition to this, as the debt-to-GDP ratio increases, the default risk of state bonds increases, increasing states’ interest expenses even more. This pressures economic growth, since this money could have also been spent on stimulating economic activity instead. If the higher expenses are financed by issuing more debt, then this cycle repeats itself and the debt level increases exponentially until it becomes unsustainable. An example of a country that was subject to an unsustainable debt level, was Greece, after the financial crisis of 2008.
As mentioned earlier, the discussion on whether states should be able to file
bankruptcy or not, has recently become more openly debated. In April 2020, the US President Donald Trump tweeted his concerns why ‘the people and taxpayers of America (should be) bailing out poorly run states (like Illinois, as an example) and cities’. He tweeted this at a time where states are running extremely high deficits in order to protect the economy after the Covid-19 virus measures. Around the same time, US Senate majority leader Mitch McConnell also addresses his critical claim that states should be able to declare bankruptcy. The question remains whether it is beneficial that states are not able to file bankruptcy, which this study might provide an answer for.
In this study, different states’ debt level will be analyzed. Even though much emphasis has been put on how and why the US’ debt level is high, not much research has been done about the consequences of this high debt level within the US itself. It is an important question to know whether high debt levels are beneficial or not to maintain economic growth for the US. This raises interest in what the consequences are of the US’ debt level on economic performance on a state-level. These results are necessary to make proper fiscal policies, especially in a high debt country such as the US.
In this study, therefore, it will be investigated what the economic effects of public debt levels in the US are. It will be analyzed within the US, comparing all fifty states’ debt level over time.
Literature review
The literature review section is structured as follows. Firstly, the common results by studies on the effect of debt on GDP will be described. Secondly, the debt threshold and its influence factors will be explained. Thirdly, channels through which debt affects economic growth will be discussed. Fourthly, differences in results for economically developed and developing
countries are discussed. Fifthly, it will be discussed whether results differ for certain economic characteristics. At last, it will be described why current sociodemographic
characteristics may be a reason for concern for future debt levels. For every mechanism that is explained in this section, national and state level conclusions are expected to entail the same results, and are therefore used interchangeably, except mentioned otherwise.
Some studies find the relationship between public debt and economic growth to be nonlinear; meaning public debt increases economic growth until a point where, above the threshold, any additional public debt results into negative economic growth. See, for example, Checherita-Westphal and Rother (2012) and Liu and Lyu (2020) who found the threshold to be a debt-to-GDP ratio of approximately 90 to 100 percent. Cecchetti, Mohanty and Zampolli (2011) find a slightly lower threshold of around 85 percent. Reinhart and Rogoff (2010) found the threshold to be 90 percent of GDP, however, their results should be interpreted with caution. After publication, the study’s internal and external validity are questioned by many researchers. Among others, Herndon, Ash and Pollin (2013), who replicated the study, removed systematic mistakes and found different results for the high debt level category (debt-to-GDP levels of over 90 percent). They found that the marginal return for additional debt is positive, but diminishing, even for the high debt category (in their regression, they found an effect of 2.2 on debt levels over 90 percent of GDP, whereas Reinhart and Rogoff (2010) found this effect to be -0.1).
In the range of national debt levels that are regarded as relatively low (debt-to-GDP ratios below 90 percent), almost all prior research suggests that higher debt levels lead to higher economic growth, although the effect is concave. This could be concluded from Reinhart and Rogoff (2010), Herndon, Ash and Pollin (2013), Liu and Lyu (2020), and Checherita-Westphal and Rother (2012). Their samples of countries are wide-ranged in different aspects, and thus the results could be generalized for other countries too.
Liu and Lyu (2020) investigated what determines the level of the above-mentioned debt threshold, and point out that this differs across countries. They found, for instance, that improving the current account balance for developed countries raises the debt threshold (meaning the debt level can be higher before the marginal return decreases or becomes negative). A current account improvement generally implies a higher rate of net export as a fraction of GDP. Trade openness is economically profitable for countries in different ways. One of them includes an increase in governments’ tax revenues, which reduces risk premia on bonds, and therefore reduces interest expenses, raising the debt threshold.
Thus, most researchers find a positive effect of public debt on economic growth, especially in the low debt level category. This is intuitive, since government expenditure financed by issuing debt can stimulate the economy by an amount higher than government spending itself, through the government expenditure multiplier. Government expenditure increases employment, investment and consumption, which can create a cycle of economic output stimulation over and over again. Therefore, under normal circumstances and relatively low levels of public debt, debt creates more economic benefits than it does economic damage.
An important issue is through which channels the level of public debt increases economic growth. Checherita-Westphal and Rother (2012) studied debt levels in different European Union member states and found that especially
(i) total factor productivity (ii) public investment (iii) private saving
were significant channels through which public debt increases economic output. Explanations for these mechanisms are given as follows. For (i), government expenditure is expected to improve the competitiveness of businesses through a more developed economic climate (which creates economic growth). For (ii), a higher government expenditure implies a higher
government investment, which stimulates economic growth (apparently, the mechanism has a stronger effect on long-term expenditure than short-term expenditure). And for (iii), a higher government expenditure provides households with more purchasing power, of which they partly spend on saving, which is beneficial for economic growth. Another approach to this, is that government expenditure provides businesses with more leverage, which protects them from negative financial shocks, and sequentially benefits economic growth as well.
A potential issue with a simple regression of public debt on economic growth is the possibility of reverse causation in the results. This may be the case if both public debt and the GDP level directly affect each other. This will likely be the case; on the one hand, increasing public debt will stimulate economic output through the government multiplier, and on the other hand, an increase in output implies an increase in taxation revenues for the government, which gives space to pay off existing public debt. Most studies in the fiscal policy field acknowledge this endogeneity problem and are usually solved by using an Instrumental Variable regression strategy. The most frequently used instrument for this IV regression is the lagged debt level (used by Checherita-Westphal & Rother, 2012; Kumar & Woo, 2010 and Liu & Lyu, 2020). The average debt levels for all the other countries in the sample is also used as an instrument in an alternative regression by Checherita-Westphal & Rother (2012).
The effect of public debt on economic growth may sometimes be different for
developing and developed countries, especially with regards to the threshold where a positive economic effect turns into a negative effect. The effect for low levels of public debt, is usually similar for developing and developed countries. Liu and Lyu (2020) conclude that there are differences for the debt threshold in developing and developed countries, which may be due to multiple reasons. For example, developing countries usually have unstable economic growth and/or weak institutions, which increases the risk premia on sovereign interest rates, and lowers the debt threshold.
A potentially important factor that should be acknowledged is the effect of additional public debt, given different economic conditions. Adelino, Cunha and Ferreira (2017) conclude that, especially coming from a period of underutilization and low interest rates, increasing public debt can highly improve economic output and employment in US
municipalities. Therefore, in regions subject to such conditions, increasing debt has a higher effect on economic growth than in regions with other conditions.
Given the results about the debt threshold and sociodemographic trends, Cecchetti, Mohanty and Zampolli (2011) point out that there may be a reason for concern. Since especially developed countries now are characterized by an increasingly ageing population, this could lead to a substantial rise in public debt and interest rates. This, then, leads to an even higher public debt level again. As an older population implies lower economic growth and an accelerating debt level, (local) governments need to act quickly and act upon their fiscal problems before the debt level becomes unsustainable (Bloom, Canning & Fink, 2011).
All in all, most research done in the field of fiscal policy, specifically the effect of public debt on economic outcomes, suggests that increasing debt for countries with relatively low levels of debt (mostly below 90 percent of GDP), stimulates economic output. For levels of debt that are higher than the debt threshold (in most studies over 90 percent of GDP), increasing debt leads to lower or even negative economic growth. Since almost all prior research on debt dynamics focused on cross-country comparisons, this study will focus on a more local level. It will also be investigated whether there is a debt threshold such as there exists on a national level, and if so, what the level of this threshold is. A comprehensive regression model will be used to draw conclusions on this.
Since local debt levels of US states are sometimes on a dangerously high level, and since they are not able to file for bankruptcy1 (and are therefore not directly incentivized to
maintain a sustainable public debt), it is expected that, after a certain threshold, additional public debt will lower economic growth. It is expected that, for relatively low levels of debt, increasing debt to finance government expenditure is beneficial, due to the government expenditure multiplier effect, but when the debt is higher than a certain threshold, debt is going to accelerate and will weaken economic growth.
Methods
The effect of the level of public debt on economic growth will be compared in all fifty states of the US. This sample was chosen because they are easily comparable; they all have the same currency for instance. Since the different states in the US are wide-ranging in
characteristics, comparing different states is interesting because a certain level of variation is expected. Data on debt and GDP were available for different states from 1960 until 2017, and are obtained from publicly accessible official US databases.
As previously mentioned, reverse causality is likely to be present in the data. This would be the case if both debt and GDP levels directly influence each other, and there is sufficient economic intuition to assume this. A primary deficit will both, in normal times, increase total debt and stimulate economic growth. Simultaneously, GDP growth, by definition, leads to higher tax revenues for governments, which gives governments space to pay off existing debt levels. Since this reverse causation is likely to be present in a standard
1 Unlike states, cities and municipalities in the US are able to file bankruptcy. For example,
the city of Detroit had a substantially high debt level in 2013 that it was forced to declare bankruptcy.
regression model, an IV technique is used. For both the variables of debt (debt and debt squared), a 2SLS instrument is used, which will be elaborated on later.
Almost all variables contain large numbers in absolute terms, and are therefore most probably subject to outliers and heteroskedasticity. Therefore, it is chosen to measure all variables (except for the dependency ratio and export-import ratio) in their natural logarithms. Later on in this study, those and more potential statistical problems will be tested.
As already mentioned, the dependent variable of the regression is the natural logarithm of GDP, and the independent variable of interest is state-level total public debt, also measured in natural logarithm form. The total public debt squared is also added to the regression (again in natural logarithm), to control for nonlinearity.
As both state population and the dependency ratio are included in the regression, there might be a multicollinearity issue present: if the population of a state grows, this means (in the short run) a larger share of the population will be younger than 18, which increases the dependency ratio. Therefore, the presence of multicollinearity in the variables will be tested later on in this study. If this appears to be a problem, an appropriate solution will be found to solve it.
Since the data used are cross-sectional series data, the possibility of
time-invariant effects that affect GDP across states should be controlled for. In the study, therefore, it will be investigated whether a fixed effect or random effect technique is necessary to be used, by the Hausman test. In the case of a fixed effect technique, a dummy variable will be added to the regression for each state (except for one), capturing economic changes for individual states over time.
Several control variables are used in the regression. These include the states’ population, income taxation, the dependency ratio and trade openness.
The following regression model will be executed:
lnGDPit = α + β1 ⋅ lnDebtit + β2 ⋅ lnDebt2it + β3 ⋅ lnPopit + β4 ⋅ lnTaxit +β5 ⋅ Depit
+ β6 ⋅ Openit + ui + εit
where i indicates the states and t the amount of years.
It is expected that, for relatively low levels of public debt, issuing additional debt is beneficial for economic growth. This holds until a certain threshold is reached where, at some level of public debt, issuing additional debt will negatively impact economic growth. Because of this nonlinearity expectation, an additional squared debt variable is included. Therefore, it is expected that β1 will be positive (and β2 negative). In statistical terms:
H0: β1 > 0
H1: β1 ≤ 0
Moreover, for the control variables it is expected that population reduces GDP growth (β3 < 0), taxation reduces GDP growth (β4 < 0), the dependency ratio reduces GDP growth (β5
< 0), and trade openness increases GDP growth (β6 > 0).
Data
In the data section, some issues with regard to the measurement and availability of data will be discussed. After this, all used variables will be operationalized and described, and the summary statistics will be given. Finally, some statistical tests are performed.
After obtaining debt and GDP levels from different sources, debt levels (provided by the US Census Bureau) were denoted in nominal terms, and GDP levels (provided by the Bureau of Economic Analysis) were denoted in real terms, fixed for current prices. This is
why another dataset from US Government Spending is used, that denotes both variables in nominal terms.
The data obtained includes all fifty states of the US. Unfortunately, some control variables have a rather limited time span compared to the other variables. Data on GDP, debt, population and taxation are available from 1960 until 2017. However, trade openness and the dependency ratio data were available from 2010 (with a few older years from trade openness as well).
The GDP level will be measured in total nominal terms and is obtained from the official data source US Government Spending. The measurement of debt and GDP can take on many forms (for example, debt as total debt, debt divided by GDP, debt per capita, the yearly change in debt). Some of these would lead to errors in the regression. For example, if debt/GDP would be chosen as the independent variable, and GDP growth would be chosen as the dependent variable, it is easy to see that any change in GDP would lead to a simultaneous change in both variables, without any underlying economic meaning. This would have led to biased and inconsistent estimators. Since GDP is chosen as the dependent variable, the debt level should not be directly affected by GDP. The same holds for GDP/capita since states’ population is included in the regression as well, which would have led to large
multicollinearity between the variables. This is why, in the end, the total amount of debt and GDP are chosen as the independent and dependent variables, respectively. Both variables will be measured in natural logarithm form in all models.
In other literature, the most common solution for this measurement problem is to use both total GDP and debt levels (see, for example, Eberhardt & Presbitero, 2014). Another solution is taking the average total GDP level for periods of five years (Kumar & Woo, 2010 and Liu & Lyu, 2020) or to use a lagged debt ratio as the independent variable (Cecchetti,
Mohanty & Zampolli, 2011). These papers use those alternatives as IV instrument, since the high probability of simultaneous causation.
As described earlier, reverse causality is likely to be present in the data, and therefore an IV strategy is used for both the debt and squared debt variables in all models. The lagged debt level and squared lagged debt level (from one year ago) are used as instruments for the debt level and squared debt level, respectively. Given that the lagged debt level is correlated with the endogenous independent variable (generally, debt levels do not change substantially from one year to the other), the instrument likely meets the relevancy criterion. This criterion will be tested later on in the data section. Moreover, given that the lagged debt level does not affect economic growth directly, but only through its impact on the current debt level, the instrument likely meets the exogenous criterium as well. And lastly, since the lagged debt level does not share common causes with GDP, the instrument is likely to be independent too.
The economic openness of a state will be proxied by the export-import ratio, obtained by trade data from the International Trade Administration. The economic openness of a state is expected to have a positive effect on economic growth and will be measured by total yearly exports divided by total yearly imports. Measuring economic openness by net exports would be possible as well, but for this, the natural logarithm form would have to be used. Since net exports partly contain negative values, the natural logarithm would not exist for a share of the data. This is why the export-import ratio is used instead. Data has been collected on both exports and imports, and this data captures trade between a certain state to any foreign country outside of the US. By excluding trade between states within the US itself, economic openness is best captured. This is because, states can be economically closed off from the world and still trade with other nearby states since the trade barriers between states are low.
The population variable is measured straightforwardly by the total amount of residents in a certain state. The population variable is likely to be an important control variable to
include in a regression explaining economic growth, since population has a strong impact on output, whether this is positive or negative. For example, Keynesian models such as the Harrod-Domar model predict that population growth negatively impacts economic growth (where Y denotes output, n population growth, s the saving rate, 𝜃 the capital-output ratio and 𝛿 the capital depreciation rate):
Δ𝑌 𝑌 =
𝑠
𝜃− 𝑛 − 𝛿
It is expected that, if a state has a high population growth rate, economic growth will decrease in the short-run (since the young age category is not economically active), but will increase in the long run (since as the children grow older, they start to contribute to economic activity).
The tax variable for states is measured by the total income tax per state. Income tax is chosen as a measure for a states’ tax policy since income tax is paid by all state residents (instead of business taxes which are only paid by firms). Moreover, income tax is usually the highest tax source for states. Choosing this measure will have the most representative and useful results. However, there might be an endogeneity issue with including tax in the regression, since tax is part of the government’s budget and could potentially be correlated with debt. For this reason, the tax variable is excluded in some of the models to see if the results are robust.
Some summary statistics on all used variables will be provided below. Note that some states do not levy an income tax, which is why the minimum of all tax observations is zero.
Table 1: Summary of variables
Obs. Mean Std. dev. Min Max
GDP (in millions of $)
3,016 266,363.8 1,263,831 845 19,500,000
Debt (in millions of $)
3,016 16,109.88 80,593.22 0 1,160,489
Population (in millions)
3,016 9.62 34.68 0.2 325
Income tax (in millions of $)
3,009 2,421.29 6,191.95 0 94,426
Dependency ratio 468 60.75 4.59 39.4 70.4
Export-import ratio 636 89.68 58.81 9.82 543.29
In Figure 3, the correlation between GDP and state debt is shown in a scatterplot. The relationship seems strong on first sight. Note, however, that this simple scatterplot does not directly show that public debt leads to higher GDP, and is moreover just a correlation. Several endogeneity issues need to be accounted for before any conclusions could be drawn.
Figure 3: Scatterplot on state GDP and state debt
As mentioned before, the relevancy criterion of the 2SLS instrument will be tested by the first-stage IV regression:
lnCurrentDebtit = π0 + π1 ⋅ lnLaggedDebtit + π2 ⋅ lnPopit + π3 ⋅ lnTaxit +π4 ⋅ Depit
+ π5 ⋅ Openit + ξit
(where i indicates the states, and t the years).
The first-stage estimates are tested for both the long- and short time span data, respectively represented by model (1) and (2) in Table 2.
0 1000000 2000000 3000000 GDP 0 50000 100000 150000 StateDebt
Table 2: First-stage IV estimates (OLS) (1) lnCurrentDebt (2) lnCurrentDebt lnLaggedDebt 0.9737*** (231.43) 0.9919*** (131.20) lnPop 0.0098** (3.01) 0.0157 (1.92) lnTax 0.0059 (1.86) -0.0028 (-0.54) Dep -0.0024* (-2.09) Open 0.0101 (1.09) Constant 0.2331*** (12.58) 0.2205* (2.00) Obs. 2,412 344 R2 0.9956 0.9968 t-statistic in parenthesis * p < 0.05, ** p < 0.01, *** p < 0.001 Both models use robust standard errors.
The coefficient of π1 is statistically significant and has large t values in both models.
Therefore, the instrument is proofed relevant. Assuming the other 2SLS conditions are fulfilled as well, we can argue that lagged debt level is a valid instrument for debt level, and effective to solve the endogeneity problem.
In Figure 4, the dependency ratio overviews for 2010 and 2018 are shown. A quick observation suggests that the dependency ratios are concentrated around higher categories in 2018 compared to 2010. This could be due to higher population growth (increase in the <18 age category) or an ageing population (increase in the >65 age category). The latter is more plausible and in line with a broad trend across developed nations, where an increasing share of the population is over the age of 65 (Bloom, Canning & Fink, 2011).
Figure 4: Dependency ratio for all states in 2010 (left) and 2018 (right)
Since heteroskedasticity could be present in the dataset, a Breusch-Pagan test is performed. The results for the test are:
H0: variance is constant
H1: variance is not constant
χ2 = 26.76
p = 0.0000
The null-hypothesis is rejected for any significance level. As expected, the variance in the model is not constant and heteroskedasticity is a substantial problem in the dataset. In
0 .02 .04 .06 .08 .1 D e n si ty 40 45 50 55 60 65 Dep 0 .02 .04 .06 .08 D e n si ty 45 50 55 60 65 70 Dep
order not to violate the OLS assumption of constant standard errors, robust standard errors are used in all regressions.
As already mentioned in the method section, another statistical issue that might be present is multicollinearity. This could happen for the population and dependency ratio: a growing population usually implies a higher proportion of the population being in a young age segment, which leads to an increase in the dependency ratio. Therefore, a
multicollinearity test (utilizing the variance inflation factor (VIF)) is performed to see if this leads to issues in the regression. The results indicate a low level of multicollinearity (VIF-value of 4.70 for population and 1.76 for the dependency ratio).
Since cross-sectional time-series data is used, it should be tested whether a fixed-effects or random fixed-effects strategy would suit the regression. First, a Hausman test is performed to see whether a fixed or random effects strategy is more suitable, based on whether the unique errors (ui) are correlated with the estimators. If they are, a fixed-effects
technique is preferred over a random effect strategy. The Hausman test results are: H0: unique errors (ui) are not correlated with the estimators
H1: otherwise
χ2(6) = 693.45
p = 0.0000
Thus, the null-hypothesis is rejected for any significance level. The unique errors do correlate with the estimators, implying a fixed-effect strategy is preferred over a random effects strategy. To check whether this fixed-effect strategy is preferred over a standard OLS regression, an F-test is performed to check if the fixed effects are jointly zero or not:
H0: all fixed effects are jointly zero
H1: otherwise
F(42, 295) = 106.34 p = 0.0000
The null-hypothesis is rejected for any significance level; fixed effects need to be accounted for in the regressions. Therefore, in all models, state-specific dummy variables will be added to the regression, controlling for unobserved state-specific characteristics. The dummy variable captures a fixed effect for the GDP level specific to any state over time.
Results
Multiple regression models were performed to answer the main research question on whether public debt is beneficial for economic growth or not. The different models include different control variables and are also different because of their time-range. For the population and tax rate variables, the data has a wide time range (from 1960 until 2018). For the dependency ratio and economic openness (export-import ratio), however, the data has a relatively short time-range (respectively nine and thirteen years).
Starting with model (4) in Table 3 (one of the long-term models), a strong indication that debt is beneficial for economic growth is found. Moreover, since the squared debt variable is statistically significant, the effect of debt on GDP is nonlinear. Its coefficient is positive, meaning the positive effect of debt is even stronger for higher debt levels, implying an increasing and concave relationship.
Since both the debt and GDP variables are noted in their natural logarithms, the
coefficient β1 and β2 are interpreted as an elasticity. For example, a one-percentage increase in
debt will increase GDP by 0.14 percent, and a two-percentage increase in debt will increase GDP by 0.33 percent (based on model (4)).
Since the positive effect of debt on economic growth does not turn into negative for high debt levels, as is sometimes observed in other studies, no debt threshold is found.
Table 3: Fixed-effect regression results (1) lnGDP (2) lnGDP (3) lnGDP (4) lnGDP (5) lnGDP lnDebt 0.3220*** (20.91) 0.1168** (3.45) 0.2559*** (16.18) 0.1199*** (4.12) 0.0373 (0.55) lnDebt2 0.0622*** (23.23) 0.0510*** (13.17) 0.0237*** (4.28) 0.0017 (0.88) lnPop 1.5779*** (4.20) 1.1370*** (4.14) 1.2716*** (4.12) 0.8398*** (5.05) lnTax 0.3903*** (5.02) 0.3270*** (4.31) 0.3051*** (5.31) Dep 0.0205*** (3.83) Open -0.0254 (-0.78) Constant 7.9057*** (76.00) 5.6456*** (24.16) 7.2572*** (30.52) 6.1503*** (25.22) 6.9445*** (12.45) σu 0.6843 1.1371 0.8577 0.8651 0.3140 σε 0.4143 0.2690 0.3820 0.2439 0.0381 ρ 0.7318 0.9470 0.8345 0.9263 0.9855 Obs. 2,958 2,446 2,958 2,446 344 R2 0.7384 0.8471 0.8210 0.8844 0.9376 t-statistic in parenthesis * p < 0.05, ** p < 0.01, *** p < 0.001 All models use robust standard errors.
Based on models (1) to (4), the hypothesis that debt is beneficial for economic growth has been accepted. However, the squared variable of debt is positive and statistically
significant in all models, except model (5), which was not expected in the hypothesis. This implies that the marginal return of debt increases as debt accumulates. This contrasts most prior research, that usually finds the reversed effect.
As already mentioned, the debt variables are positive but not statistically significant in model (5). This model represents the short-run relationship (from 2010 to 2018) between public debt and economic growth and is based on a smaller sample, which might be a reason why these estimates are less precise. Also, since more control variables are included in this model, the effect of public debt might become insignificant if those control variables are better explanatory variables for GDP than public debt.
The effect of population shown in the models is also in contrast with the hypothesis. In all models where it is included, its coefficient is positive and statistically significant.
Logically, higher populated states will almost always have a larger GDP. Another explanation is that an increase in population increases the labor force, benefiting economic output.
The same holds for the dependency ratio, which has a positive significant coefficient in model (5), although it was also expected to have a negative coefficient. This might be counterintuitive, and could be a topic for future economic research.
When the potentially endogenous regressor lnTax is excluded from model (4), in model (3), the coefficient of taxation and all other variables are still statistically significant. However, for the debt variables, the t-values decrease substantially if taxation is included, which could be an indication that, to some extent, the variable is indeed endogenous. Since all other variables in the model are still significant and the low VIF-values found earlier, this problem does not seem to have a large impact on the results.
Since the obvious multicollinearity between lnDebt and lnDebt2, the squared variable
was excluded in model (2) to see how this would impact the results. Compared to model (4), it is clear that the variable does not influence the other regressors substantially. As the coefficient for squared debt is positive and significant, the relationship appears to be nonlinear. Including the squared debt variable is therefore beneficial to explaining the variance of GDP.
Another aspect that might be surprising is that the variable for economic openness (the export-import ratio) is not significant in model (5) where it is included. This is especially surprising since net export is part of GDP and therefore by definition should have a strong positive impact on GDP. More research is necessary to draw conclusions on the reasons behind this. Potentially, since the US is traditionally characterized by an import-intensive country, exports compared to imports are so small that any additional export does not have much effect on economic growth anymore.
All in all, since it appeared unnecessary to exclude both the tax and the squared debt variable, the most representative of the true relationship between public debt and economic growth are likely to be models (4) and (5), which represent the relationship in the long- and short-run relationship respectively. Public debt has a statistically strong effect on economic growth for all debt levels in model (4), and its marginal effect is even increasing. This is in contrast with most prior cross-country studies, that find a lower or even negative effect for the high debt category.
When a shorter time span is used, and more control variables are included (in model (5)), the effect is still the same but not statistically significant anymore. In contrast with most prior studies, no ‘debt threshold’ is found where any additional debt leads to lower economic growth, since the effect never becomes negative in all models. Population growth, the
dependency ratio and taxation all have a significant positive effect on economic growth in states. Trade openness, however, does not.
Discussion
In this study, the effect of public debt on economic growth is investigated. Data is obtained from all individual states in the US, from 1960 to 2017. In the log-log models, where an IV as well as fixed-effect strategy is used, it is shown that debt has a significant positive effect on GDP, for both low and high debt levels. The effect is even stronger for high debt levels, implying a nonlinear relationship with increasing marginal returns of debt. This is in contrast with most prior cross-country comparison studies, that found decreasing marginal returns of debt.
This study uses a sample of all fifty states in the US. Debt ratios (as a fraction of GDP) that states have are usually low compared to the debt ratios countries have. Therefore, the external validity of this study is low and generalization of the found results to other samples (especially cross-country) should be done with caution. This could be seen as a weakness of this study; however, it might be interesting to see whether our results are generalizable for another state setting (for example, states within Spain or Australia).
Another aspect of the results that should be noted is that this sample was based on the states of the US, which is a developed country. Debt dynamics results might be different if a sample was used from a developing country. As shown by Liu and Lyu (2020), the results will most probably be more negative for high debt levels.
What has not been carried out in this study, but might still be interesting to see is, creating different regression models for low, medium and high debt categories, and to see how the coefficients change between the categories. It would be expected that, for the high debt category, the coefficients are higher than for the low debt categories.
For further research in the fiscal policy field, another dataset could be used where data on trade openness is more widely available. Since in this dataset, only thirteen years are used on this variable, it is not yet clear what the true effect is if such a variable is included with a wide time span. Moreover, since the coefficient for economic openness is negative and not statistically significant (whereas it was expected it would be significant and positive), more research is necessary to find out whether net export is a valid control variable in this
regression.
Another aspect that requires more research is why an increase in the dependency ratio significantly increases economic growth. Intuitively, one would expect that a higher
dependency ratio (since a larger share of the population is in an age category where they are not economically active) decreases economic growth. Perhaps the short time span in this sample caused the variable to be less precise than the relationship is in reality. More research should be done about this.
Conclusion
This study investigated the effect of public debt on economic growth, based on a sample of all US states since 1960. In most fixed-effect models, this effect is positive and statistically significant. For higher debt levels, the positive effect on economic growth is even stronger; implying a positive concave relationship with increasing marginal returns. Therefore, the null-hypothesis that debt has a positive effect on economic growth for small debt levels, has been accepted. The found result is in contrast with most prior cross-country literature, which usually finds a lower or even negative effect for high debt levels.
All states in the US are legally not able to file bankruptcy, although recently several political leaders (including US President Donald Trump) have stated that changing this law
might be a good idea. Given the results found in this study, there is no indication that this law should be changed.
An IV regression strategy is used in all models, since the strong potential for reverse causality between public debt and GDP. The 2SLS instrument used is the lagged debt level from year t-1. The squared debt level (included to control for nonlinearity) is also
instrumented, with the squared level of lagged debt (also from year t-1).
In all models, a fixed-effect strategy is used. Data were tested to contain state-specific fixed effects, which is why all models contain fixed-effect dummy variables.
The results appear to be partially robust for different control variables and time spans. When control variables are added that could potentially affect economic growth, the debt variables remain positive in all models, and statistically significant in almost all models (except for model (5)). This model has a short time span (2010 – 2018) and included all the control variables. A potential reason why in this model the effect is not statistically significant is, because it uses a short time span, the results are less precise. Alternatively, it may be an indication that there is no strong relationship between debt and GDP, but that the majority of the variation in GDP is explained by increases in population, taxation and/or the dependency ratio.
In this study, multiple statistical tests were performed to check if the models were subject to endogeneity. Heteroskedasticity appeared to be present in the dataset, which is why robust standard errors are used in all models. The variable for taxation was potentially
multicollinear since the variable could be correlated with public debt directly. However, after excluding this variable in two of the five models, results in the models where taxation is included, were all still statistically significant (although t-values decreased for the rest of the regressors).
Since the increasing trend of dependency ratios in developed countries (caused by an ageing population), future debt levels will likely increase. An ageing population implies higher social security expenses for governments, along with lower taxation revenues
(especially income tax). For states in the US, there is no immediate cause for concern (given the current debt levels and the found results); however, fiscal policymakers should keep an eye on the debt trend the coming years to prevent debt accumulating unsustainably in any of the states.
Given the found results, the current situation of the debt levels of states is not too alarming. Therefore, the urge of President Trump’s message that states should be able to go bankrupt if their debt is too high, does not seem to be justified. However, states should always be aware of piling up public debt, especially given the increasing dependency ratios the coming years, in order not to let debt grow unsustainably. At the moment, it is not forecasted that this will happen in any of the states in the coming years.
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Appendix
Table 4: test for multicollinearity, given by VIF-values
Variable VIF 1/VIF
lnDebt 10.14 0.0986 lnPop 4.70 0.2129 lnTax 4.00 0.2501 lnDebt2 3.09 0.3232 Dep 1.76 0.5685 Open 1.43 0.6981 Mean VIF 4.19
Table 5: Hausman test for fixed and random effects
Coefficients (b) fixed (B) random (b-B) Difference S.E. lnDebt 0.0373 0.0789 -0.0416 0.0170 lnDebt2 0.0017 -0.0018 0.0035 . lnPop 0.8398 0.7376 0.1021 0.1198 lnTax 0.3051 0.2203 0.0849 0.0110 Dep 0.0205 0.0244 -0.0039 . Open -0.0254 -0.0381 0.0127 . χ2 (6) = 693.45 p-value = 0.0000
