EXTERNAL DEBT SUSTAINABILITY OF U.S: A NONLINEAR APPROACH
The main objective of this paper is to carry out an investigation of the sustainability of external debt of US through a non-linear approach. We are first going to test the non-linearity and non-stationary nature of the data simultaneously. We are then going to test the linearity of the ratio against the threshold autoregressive using the TAR model. The US debt sustainability has been an issue of global concern for quite some time now. We are going to analyze it using the MS unit root test which is applied to the debt flow for the current account. The MS root test is going to be used in order to examine the local stationary and global stationary of the debt. The TAR model provides us with some new insights on the issue of the US external debt in the recent past. It suggests that even though the debt/current account GDP ratio may remain relatively high, the probability of sustainability can be expected to be high when the recent dollar depreciation is also taken into account. External debt is not healthy for any economy whether developing or a developed economy. Even though it may be a source of revenue for financing various projects in the country, countries should try to avoid the amount of external debt subjected to their economy. A country’s external debt sustainability refers to whether a country is able to meet its foreign debt liabilities.
External debts are one of the barriers to economic and social developments of both the developing and the developed countries. Fiscal policies, sustainability and solvency have therefore become some very important issues that any country that wants to achieve sustainable development will take into consideration during planning of various activities in the country. Domestic debt was the main source of financing for the closed economy. US can be regarded as a closed economy and its main source of financing was the domestic debt. However, there have been changes and the US has also ventured into external debts thus allowing it to take financial aid from other external monetary institutions so as to help it sustain its economy. In the 1980s, during the time of foreign debt crisis years, USA experienced some constant account deficits as a result of the hard economic times during the period. Foreign debt sustainability can refer to a situation whereby a country is able to meets its foreign debt obligations. If the present value of a country’s future foreign earnings is equal to the current value of its foreign debt, then it can be said the country’s foreign debt is sustainable otherwise it is unsustainable (Mohammadi et al., 2007). In order to achieve sustainability in the debt ratio, the total external debt to the GDP has to be stabilized.
The objective of this study is to test for the sustainability of the US external debt through the use of nonlinearity methods. The paper is divided into five different sections in an attempt to analyze the US eternal debt sustainability. The sections include: Section I – providing a historical analysis and development of the US in terms of external debt for the period 1990 1st Quarter to 2009 4th Quarter, Section II –Literature Review, Section III – deals with the econometric methodology, section IV – presents some form of empirical results from the studies conducted about the current state and the past state of the US as per the external debts and Section V – has the conclusions and a summary on whether external debt is sustainable in the US or not.
Section I – The Development of the US External Debt
The United States economy also needs external debt for its development and in order to be able to finance some of its operations both within the borders or other missions outside the boundaries of the nation. As per a report issued on 30th June 2011 by the World Bank, the US was leading with the amount of external debt that it had. The amount was estimated to be 14,825,308,000,000 USD.
The graph shown below shows the annual data for the US public debt as a percentage from 1929 to 2006.
Section II - Literature review
External debt is the amount of money that is owed to creditors outside a given country. There is a lot of literature that exists pertaining to the subject of external debt. In this section we are going to look at various definitions of external debt as proposed by different scholar. We are then gong to look at literature covering various aspects of external debt and whether the United States of America has a sustainable external debt.
According to (Hansen, 2001), the Gross External debt at any given time is the amount of money that is owed by a country to nonresident financial institutions or country. He adds that sustainable debt analysis refers to a level of debt that can allow a debtor to meet its current and future debt obligations without looking for ways of getting debt relief.
The motivation of studying and revisiting the U.S debt problem is clearly stated in the Economic Report from President. Widespread use of U.S dollar plays a significant role in the global financial market. The final step in winning the future is to make sure we aren’t buried under a mountain of debt.
The United States is often viewed as a massive debtor to the world. Foreign investors own only about 11 percent of the overall financial assets in the U.S. economy and own roughly one-third of U.S.
Excessive accumulation of debt, both public and external, can eventually become a problem economically as it can lead to financial crisis. On the other hand, debt is not always bad. "If you're running debt because you have an investment movement and lots of capitalist spending, and you don't have domestic savings, then borrowing from abroad for investment is good news. But when borrowing to consume, like the U.S. consumer has done, or borrowing to spend more than your tax revenues, which the U.S. government has done, the situation can be eventually unsustainable."(Roubini 2008).
In the argument of history matters that a country's record at meeting its debt obligations and managing its macro economy in the past is relevant to forecasting its ability to sustain moderate to high levels of indebtedness, both domestic and internal, for many years into the future. The concept of "debt intolerance", which manifests itself in the extreme duress many emerging market economies experience at overall debt levels that would seem quite manageable by the standards of the advanced industrial economies (Reinhart C. M., Rogoff K. S., Savastano M.A. 2003).
They discussed about a country's external debt intolerance can be explained by a very small number of variables related to its repayment history, indebtedness level, and history of macroeconomic stability. Markets view highly debt-intolerant countries as having an elevated risk of default, even at relatively low ratios of debt to output or exports. Whether markets adequately price this risk is an open question, but it is certainly a risk that the citizens of debt-intolerant countries should be aware of when their leaders engage in heavy borrowing. Understanding and measuring debt intolerance is fundamental to assessing the problems of debt sustainability, debt restructuring, and capital market integration, and to assessing the scope for international lending to ameliorate crises.
External debt sustainability analysis generally conducted in the context of medium-term scenarios, and one advantage of medium-term scenarios is that borrowing is viewed within the overall macroeconomic framework. Secondly, debt ratio have been developed mostly to help indicate potential debt-related risk, and thus to support sound debt management. Likewise, the debt-to-export ratio can be used as a measure of sustainability because an increasing debt-to-exports ratio over time, for a given interest rate, implies that total debt is growing faster than the economy, indicating that the country may have problems meeting its debt obligations in the future.
Cunningham (1993) investigated the relationship between debt burden and economic growth for sixteen countries for the period of 1971-2007. The study shows that growth of a country's debt burden has a negative effect on the economic growth. Also, on the point of view that current debt inflows as a ratio to GDP, past debt accumulation and debt service ratio have affected economic growth adversely (Elbadawi 1996). One research on sub-African countries examines the relationship between economic growth and external debt for the period 1970-1986. The study reveals that on average a high debt country faces about one percentage reduction in the GDP annually (Fosu 1996).
The widest notion of sustainability of debt growth is one setting a limit not on the level of the debt ratio but on its long-run growth rate. Luig Spaventa (1987) found out that even if there are no limits to the tax burden that the community is ready to bear for servicing the debt, or if such limits are neglected, the constraint is not sufficient to establish a condition of sustainability when the size of the debt affects the real interest rate in the medium run. When it does, as is probable in the case of finite horizons, a given fiscal rule may become less sustainable with time and may eventually turn out to be unsustainable even in the widest sense of the budget constraint.
Many economic models and econometric technique used by previous empirical studies. Karagöl (2002) examined relationship between economic growth and external debt service for Turkey during 1956-1996. The author used multivariate co-integration techniques. The study shows that there exists a negative relationship between external and economic growth in the long run. Granger causality test results showed a uni-direction causality running from debt service to economic growth. Three-gap dynamic model of macroeconomic models of macroeconomic equilibrium has been used by Ahmed (2001) to analyze the external debt problem of Pakistan. A robust test of sustainability is presented using a nonlinear representation of the debt–GDP ratio to assess whether the UK public finances were sustainable for the period 1919-2001. In the paper called U.S external debt sustainability revisited: Bayesian analysis of extended Markov switching unit root test, the author used a Markov switching (MS) unit root test to analyze the sustainability of U.S external debt. Firstly, he apply the MS to examine local stationarity and global staionarity. The contribution he did in the paper was to extend MS unit root test where the transition probability is time-varying rather than fixed. When recent U.S dollar depreciation is taken into account, the debt/current account-GDP ratio remains relatively high, and the probability of stationarity (sustainability) is unexpectedly high. In the paper, the author compared three models to find out the most appropriate one among TVTP with fixed variance, FTP with fixed variance and the Bayed factor (BF). The result came up with the TVTP with time-varying variance model is the most appropriate model to assess the probability of the sustainability of U.S external debt (Takeuchi 2010).
In Yilanci and Özcan's (2008) paper, they use a two-regime threshold autoregressive (TAR) model with an autoregressive unit root to estimate the external debt sustainability of Turkey. The threshold autoregressive model is one of the nonlinear time series models available in the literature. It was first proposed by Tong (1978) and discussed in detail by Tong and Lim (1980) and Tong (1983). The major features of this class of models are limit cycles, amplitude dependent frequencies, and jump phenomena. Much of the original motivation of the model is concerned with limit cycles of a cyclical time series, and indeed the model is capable of producing asymmetric limit cycles. The threshold autoregressive model, however, has not received much attention in application. This is due to the lack of a suitable modeling procedure and the inability to identify the threshold variable and estimate the threshold values (Tsay 1989). Researches choose different techniques for modeling depend on many criteria, such as if data hold the assumptions, consideration of the uncertainties, therefore, there is no perfect data, neither perfect model.
Section III - Econometric Methodology
In this section we are going to use some two-regime threshold autoregressive model (TAR model) with an autoregressive unit root (Caner & Hansen, 2001).
It is given by the formula:
For t=1….T, et is an i.i.d error and the 1(.) is the Heaviside indicator which will take the form:
Using the TAR model to investigate the US external debt sustainability
The TAR model can be represented using the following formula
In this case, st-k will be the state determining the variable.
The integer k used in the above subscript will determine the number of lags that the state determining variable influences the given regime at a specific time t.
When the value of st-k = yt-k , then we can say that we have achieved a self exciting TAR. There are also some possible variations of the TAR model which include:
More than 2 regimes
Alternative dynamic specifications
Switching in only some of the parameters
Different threshold variables
Consider the value the value of k = 1. In such a case the parameters that therefore need to be estimated are: m1, m2, s1, s2 and r. The estimation method that can be used to determine the values of those parameters is the least squares method. The value of r will be estimated by a grid search.
The graph shown below shows the annual data for the US public debt as a percentage from 1929 to 2006.
The graph below shows the threshold
In order to find the threshold error correction we use the following formula as obtained from the EVIEWS program:
series y = d(r120)
series x = d(r3)
series spread = r120 - r3
scalar th = 3.22
series _d = ( spread(-1) < th )
equation tar.ls y c y(-1) y(-2) x(-1) x(-2) _d*spread(-1) (1-_d)*spread(-1)
Section IV- Data Section Empirical Results
When handling this section we are going to use the time series data of the ratio for the US net external debt stock to the GDP. The data sets to be used comprises of quarterly observations over a period from 1990 to 2009. The data has been obtained from United States of America Central Bank Reserve.
The amount of public debt has increased substantially for different countries at all income levels due to the current global economic crisis. The historical data obtained from various financial institutions, show that there is an increase in debt for the years the followed the financial crisis. Most of the projections that are being issued by the World Bank on several countries show that debt levels is unsustainable for several countries. The increase in external debts is also resulting into a stagnation of development for various developing countries. When an analysis is conducted, a threshold of 90% after which the real economic growth of the economies start to decline. This 90% threshold has very practical significance since the United States and other developed nations are projected to attain it soon and remain above it for some years.
There are several reasons why debt threshold may vary for different countries. This section is dedicated towards analyzing the threshold in long-term average public debt to the GDP ratios. In order to calculate the threshold, we are going to first take a country’s initial GDP, inflation and trade openness.
This section is further subdivided into four sub-sections namely: the data, methodology, results and the conclusion.
a) Data section
The data that was used in this study was obtained from a dataset of 26 developed countries and 75 developing countries. A large group of developed and developing countries was used so as to help in improving the accuracy of our results as a wide range of data is covered hence a fair sample for the study. The main variables used in this study are the gross public debt, GDP growth and some set of control variables which usually influence economic growth. The data that I used for the study was taken between the 2nd quarter of 2003 to the second quarter of 2011.
The table shown below shows the data that was obtained for the US only.
Period between the third quarter 2008 to the second quarter 2011
After the amount of external debt had dropped in the second quarter of 2008, the amount of external debt stated to show some increments. There has been a tremendous increase in the amount of external debt since the third quarter of 2008 up to the first quarter of 2011. There were some actions that were sought by congress in order to reduce the amount of external debt. Despite the proposals by the democrats to increase borrowing, their attempt was turned down by the republicans and hence the decrease in the amount of external debt as it can be seen from the table above.
In the study, we used the method of threshold least squares regression model. We also used the pooled least squares regression method for the analysis. The threshold estimation method is used since it is more superior to other techniques which were previously used for the estimation of the nonlinear functions. This method allows for the identification of the threshold level, its significance and the coefficients of the different regimes. It also helps in deducing the significance of the threshold from the data.
i. Threshold regression model
i- Represents the country index
The unknown threshold value l and the coefficients of β0, 1… β2, 2 are estimated using the threshold least squares method.
When estimating the threshold value, the above equation can be simplified into:
The threshold can be tested in a relationship between the long-run average public debts to the GDP ratio between the years that are being studied. There are two sets of hypothesis that are used when testing for the threshold. The null hypothesis that is used for the study here is that the slope coefficients and the intercepts are identical in the two regimes under study.
H0: β0, 1 = β2, 2, β1, 1
If there is no threshold, the above equation will not be rejected and a simple least squares model can then be estimated. However if there is a threshold effect the unknown threshold value can then be estimated.
The results obtained from the above estimations using the above equations show that there is a relationship between the long-run average public debt to the ratio of GDP and the long-run GDP growth. It is therefore very crucial to take into consideration the initial GDP. It should also be noted that the threshold level differs for both the developing and developed economies and the cost f passing the debt threshold is quite high over time.
The study carried above has investigated the short-term and long-term sustainability of the United States of America’s external debt. The methods that were used for the investigations allowed for a simultaneous testing of non-linearity and non-stationarity of the external debt. From the study, I was found that the external debt – GDP ratio is nonlinear series and suits the unit root test. Using the above mentioned two methods, we also found out that the external debt is a TAR process which has a unit root. If the ratio between the external debt and the GDP shows some increase of more than 3% between the previous quarter and the preceding quarter, then significant fiscal stabilizations will occur.
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