countries is higher than in non-OECD countries, and this means that OECD coun-tries are more dependent on trade.
In general, we can find that from 1960–2006 to 1980–2006, the macroeconomic performance and related variables deteriorate and become more volatile, and they develop into better and more stable entities after 1990. Openness is the only vari-able that consistently goes higher. On the other hand, whether classifying countries by income level or OECD membership, macroeconomic variables, including inflation and fiscal deficits, perform better and are more stable in countries in higher develop-ment, and perform worse and are more unstable in countries in lower development.
4.2 Cross-sectional results
First, the deficit-inflation linkage is examined with the long-term average data over the period covering 1960–2006. Given a specific quantile τ , the empirical model of quantile regression is
πi = x0iβ(τ ) + εi(τ ), (15) where πi is the logarithm of the average of annual inflation (log(inflation)), and inflation is measured by the percent change in the CPI index. Taking the logarithmic transformation could normalize the data and reduce the effect of the extreme data.
xi is a vector of explanatory variables, including intercepts and fiscal deficits. β(τ ) is a vector of parameters at a specific quantile τ , and εi(τ ) is an error term.
The cross-sectional results are shown in Table 4. Table 4 reports the coefficients at various quantiles from 0.1 to 0.9, and also reports the results of OLS for compar-ison. For calculating a confidence interval, bootstrapping is employed to estimate stand errors, and the number of re-sampling times is 1000. We can find that the deficit-inflation relationship is weak and not robust in the long-term average data, and this result is consistent with some previous empirical studies, such as those observed by Click (1998) and Kwon et al. (2009).
First, the theoretical model of Cat˜ao and Terrones (2005) is followed. They
mod-‧
eled the deficit-inflation relationship with scaling deficits by narrow money which stands for the size of the inflation tax base. The results are reported in panel (A) of Table 4 and plotted on the upper part of Figure 1. The black solid and black dotted lines indicate coefficients at various quantiles and the 95% confidence inter-val respectively. The grey solid line is the OLS estimate. We can see that from quantiles 0.1 to 0.9, the coefficients of the average deficit-to-money ratio are 0.5287, 0.5869, 0.5803, 0.7813, 0.7457, 0.6716, 0.8603, 0.8144 and 1.7967. From quantiles 0.1 to 0.5, the coefficients are significant at the 1% level, and significant at the 5%
level at quantile 0.6 and 0.7. However, the coefficient is insignificant at quantile 0.8.
Although it seems that the term average deficits become inflationary as long-term average inflation rises, it is not significant enough at the top quantile. On the other hand, the OLS coefficient is 0.8687 at the 1% level of significance; it indicates that average deficit-to-money ratios have a positive impact on average inflation.
Second, the standard specification of scaling fiscal deficits by GDP rather than money is estimated. The results are shown in panel (B) of Table 4 and plotted in on the middle part of Figure 1. The same black solid and the black dotted lines indicate coefficients at various quantiles and the 95% confidence interval respectively. The grey solid line is the OLS estimate. We can see that the coefficients of the average deficit-to-GDP ratios are 4.7201, 4.2520, 3.7353, 3.2610, 2.9507, 2.1895, 1.7003, 3.3068, 4.5772 and 8.1045 from quantiles 0.1 to 0.9. They are significant at the 1%
level from quantiles 0.1 to 0.3 and at the 5% level at quantile 0.4, but insignificant from quantiles 0.5 to 0.9. The OLS coefficient is 0.8687 at the 1% level of significance.
Compared with scaling deficits by money, the deficit-to-GDP ratio is significant at fewer quantiles and shows that the long-term relationship is weak. However, the OLS estimator is still positively significant.
Finally, with the standard specification of scaling fiscal deficits by GDP, the average money growth rates are controlled in equation (15), such as Kwon et al.
(2009). As inflation, the average money growth is transformed into a logarithmic
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form. The results are shown in panel (C) of Table 4 and the lower part of Figure 1.
The meanings of the black solid line, the black dotted line, and the grey solid line are defined above. From quantiles 0.1 to 0.9, the coefficients of the average deficit-to-GDP ratio are 2.5915, 1.1392, 1.0395, -0.1321, 0.1123, 0.5190, 0.6264, 0.5740 and -0.1386, and the coefficients of the average money growth are 0.6631, 1.2118, 1.2456, 1.2775, 1.2526, 1.2569, 1.2467, 1.3152 and 1.3279. All of the coefficients of the deficit-to-GDP ratio are insignificant, and all of the coefficients of the money growth are significant at a 1% level except quantile 0.1, where the coefficient is significant at the 10% level. The OLS estimates of the deficit-to-GDP ratio and the money growth are 0.6031 and 1.1724 respectively. The same, the deficit-to-GDP ratio is insignificant and the money growth is at a 1% level of significance.
Compared with previous studies, Click (1998) discovered that domestic debt has no effect on seigniorage with long-term average data, and therefore fiscal variables are not inflationary. Kwon et al. (2009) found a weak relationship between public debt and inflation over the long term. On the other hand, Fischer et al. (2002) showed that fiscal deficits positively affect inflation in the long-term average data in a full sample.
Accordingly, only when the long-term average money growth is not controlled, the OLS estimators are consistent with Fischer et al. (2002). Otherwise, the esti-mated results are weak or nonexistent. Hence, my cross-sectional results show that the fiscal deficit is weakly associated with inflation and not robust in the long-term average data, so it tends to be in line with Click (1998) and Kwon et al. (2009).
As Kwon et al. (2009) illustrated, in the long run, debt must be solved with a fiscal surplus or be monetized ultimately, and which one is chosen is determined by the policy regime (Sargent, 1982). However, the policy regime could be different in each country and change over time, so it is difficult to find a statistical linkage of fiscal variables and inflation in long-term average data.
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Since long-term average cross-sectional data cannot clarify the relationship between fiscal deficits and inflation, the panel data provides another approach to estimating the deficit-inflation relationship in the long-run. Panel data estimation contains individual time-invariant terms for controlling country-specific effects, and could allow for an intrinsically dynamic adjustment to distinguish the long-run effect.
Empirically, given a specific quantile τ , the dynamic panel quantile regression model is where πit is the logarithm of one plus annual inflation (log(1+inflation)), and in-flation is measured by an annual change in the CPI index. ηi is a time-invariant individual effect, xit−j refers to current and lagged fiscal deficits, and εit(τ ) is an error term. α(τ ) and βj(τ ) are the parameters to be estimated, and Pp
j=0βj(τ ) is what we are concerned with. Dynamic panel quantile regression of Lin (2010), which is a two-stage fitted value approach, is employed to estimate equation (16), and lagged differenced dependant variables are taken as instruments.
Lagged inflation is included on the right-hand side to capture persistence and dynamic adjustment. The fiscal deficit is scaled by narrow money, which is modeled by Cat˜ao and Terrones (2005). They scaled the deficit by narrow money rather than by GDP, because the former (narrow money) stands for the size of the inflation tax base. Thus, given a change in the deficit-to-GDP ratio, the economy in higher in-flation would be impacted by deficits more strongly, because its inin-flation tax base is typically more narrow. In addition, the fiscal deficits do not necessarily impact on in-flation contemporaneously since the government can borrow and allocate seigniorage intertemporally. Therefore, the fiscal deficit is considered to be a distributed-lag due to the dynamic relationship. Accordingly, the deficit-inflation relationship is