The baseline analysis

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 π_it is the logarithm of one plus annual inflation (log(1+inflation)), and in-flation is measured by an annual change in the CPI index. η_i is a time-invariant individual effect, x_it−j refers to current and lagged fiscal deficits, and ε_it(τ ) is an error term. α(τ ) and β_j(τ ) are the parameters to be estimated, and Pp

j=0β_j(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

nonlin-‧

ear and dynamic, so the summations of the coefficients, Pp

j=0β_j(τ ), is what we are concerned with. I choose p = 3 because p is smaller or equal to 3 in most empirical studies.⁹ For allowing the dynamic terms, the observations from 1960 to 1963 are dropped.

With the data of full samples (91 countries) over a period of 1960–2006,¹⁰ the results of taking one instrumental variable (∆π_it−1) is shown in Table 5 and the upper part of Figure 2. Standard errors are estimated by bootstrapping, and the number of resampling times is 1000.

For comparing the results of dynamic panel quantile regression, the estimates of dynamic GMM of Arellano and Bond (1991) (D-GMM L) are reported as well, where lagged levels of the dependent variable are taken as instruments. On the other hand, for comparison, I also take lagged differenced dependent variables as instruments in dynamic GMM (D-GMM D). Additionally, the number of instruments in D-GMM L and D-GMM D is in line with the number of instruments in dynamic panel quantile regression, and the differenced exogenous variables are also taken as instruments in GMM.

In Table 5,P3

j=0deficit/money_t−j is the summation of the coefficients of current and all lagged deficits (Pp

j=0β_j(τ )), and that is what we are most concerned with.

From quantiles 0.1 to 0.9, the summations of the coefficients are 0.0094 0.0165, 0.0236, 0.0272, 0.0312, 0.0369, 0.0452, 0.0660 and 0.1128. They are insignificant at quantile 0.1, significant at the 5% level at quantile 0.2 and significant at the 1% level at quantiles 0.3–0.9. We can find that the summation of the coefficients becomes larger as the quantile rises. It means that fiscal deficits have no impact on inflation when the inflation is at a low level, but deficits would be more inflationary as inflation rises. The coefficients of D-GMM L and D-GMM D are 0.0438 and 0.0853

9For example, Karras (1994) chose p = 3, Fischer et al. (2002) chose p = 2 and Cat˜ao and Terrones (2005) chose p ≤ 3.

10Data of inflation and deficit-to-money ratio are both stationary over 1960–2006. The t-statistics of the Levin-Lin-Chu test (one lag) for inflation and deficit-to-money ratio are -29.95 and -25.93 respectively.

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respectively, and both are significant at the 1% level. However, the outcome of D-GMM L the estimator is closer to the outcome of quantile regression and roughly equal to the average of coefficients at nine quantiles. The outcome of D-GMM D is apparently greater than the outcomes of D-GMM L and near to the coefficient of quantile regression at quantile 0.9.

As we can see, the estimates of fiscal deficits are shown on the upper part of Figure 2. The horizontal and vertical axes indicate quantiles and coefficients respec-tively. The black solid line represents the coefficients of the dynamic panel quantile regression, and the black dotted lines represent 95% confidence interval of the quan-tile regression. The gray solid and the gray dotted lines indicate the coefficients of D-GMM L and D-GMM D respectively. Obviously, the estimates of quantile regression are positively related to the quantile, and insignificant at low quantile (0.1).

Accordingly, the impact of fiscal deficits at various inflation levels could be observed by quantile regression, and the “high inflation rate” or “high inflation episodes” need not to be defined arbitrarily. On the other hand, the dynamic GMM estimators only show the average impact of deficits on inflation.

Compared with previous literature studies, my empirical results confirm the findings of many empirical research on the deficit-inflation relationship (De Haan and Zelhorst, 1990; Fischer et al., 2002; Cat˜ao and Terrones, 2005; Doma¸c and Y¨ucel, 2005) — fiscal deficits will be more inflationary the higher the inflation rate, and they will play a weak or non-existent role in inflation when inflation is at a low level.

Therefore, fiscal consolidation would become more effective in price stabilization as inflation rises.

In addition, the estimates of lagged inflation are also reported in Table 5. From quantile 0.1 to 0.9, the coefficients are 0.2266, 0.3102, 0.3299, 0.3677, 0.3735, 0.3697, 0.4447, 0.4531 and 0.5687. They are significant at the 5% level at quantiles 0.2 and 0.3, and significant at the 1% level from quantile 0.4 to 0.9. Hence, lagged inflation

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is significant and positively related to current inflation. This means that inflation is persistent, and the relationship between lagged and current inflation tends to be stronger when inflation is higher. Only at a low level, will the lagged inflation not affect current inflation, and inflation is not persistent.

Next, there are more lagged difference inflation terms taken as instrumental variables in equation (16). The results of taking two instrumental variables (∆π_it−1 and ∆πit−2) are shown in Table 6 and the middle part of Figure 2, and the results of taking three instrumental variables (∆πit−1, ∆πit−2 and ∆πit−3) are shown in Table 7 and the lower part of Figure 2.

With two instrumental variables, the summations of the coefficients of deficit-to-money ratios are 0.0089, 0.0151, 0.0228, 0.0277, 0.0305, 0.0344, 0.0441, 0.0650 and 0.1137 from quantile 0.1 to 0.9. They are insignificant at quantile 0.1, significant at the 5% level at quantile 0.2 and significant at the 1% level at quantiles 0.3–0.9.

The estimates of D-GMM L and D-GMM D are 0.0421 and 0.0636 respectively, and both are significant at the 1% level. With three instrumental variables, the summations of the coefficients of deficit-to-money ratios are 0.0112, 0.0145, 0.0229, 0.0268, 0.0301, 0.0364, 0.0454, 0.0656 and 0.1124 from quantile 0.1 to 0.9. The same, they are insignificant at quantile 0.1, significant at the 5% level at quantile 0.2 and significant at the 1% level at quantiles 0.3–0.9. The estimates of D-GMM L and D-GMM D are 0.0345 and 0.0473 respectively, and both are significant at the 1% level.

Compared with one instrumental variable, taking two and three instrumental variables have very similar results in quantile regression — fiscal deficits will be more inflationary as inflation rises, and fiscal deficits play no role in inflation when inflation is at a low level. Therefore, the number of al variables would not change the results. Similarly, taking two and three instruments do not change the estimates of D-GMM L a lot. However, the estimates of D-GMM D will change when more instruments are taken, so D-GMM D is not as stable as quantile regression and

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By means of a quantile regression, the advantage of scaling deficits by narrow money, which is suggested by Cat˜ao and Terrones (2005), is apparent. Given a change in the deficit-to-GDP ratio, the economy in higher inflation would be im-pacted by deficits more strongly. Furthermore, the more standard specifications, which scales fiscal deficits by GDP, are estimated with the data of the same 91 countries over the period spanning form 1960–2006.¹¹ The results are reported in Table 8 and the estimates of the deficit-to-GDP ratios are plotted on the upper part of Figure 3. From quantile 0.1 to 0.9, the summations of the coefficients of the lagged and current deficit-to-GDP ratios are 0.1704, 0.1537, 0.1734, 0.1841, 0.1936, 0.2208, 0.2843, 0.3651 and 0.5961. The deficit-to-GDP ratio is also more inflationary when inflation is higher. Although it is significant at the 1% level at quantiles 0.1–0.7 and at the 5% level at quantile 0.8, however, it is insignificant at quantile 0.9. The D-GMM L and D-GMM D coefficient are 0.3798 and 0.6236 respectively, and both are significant at the 1% level. As we can see in Figure 3, it is observable that the deficit-to-GDP ratio is insignificant at quantile 0.9 because its volatility is too large.

Different from scaling deficits by narrow money, the deficit-to-GDP ratio is sig-nificant at a low quantile (0.1) and insigsig-nificant at a top quantile (0.9), although it is also more inflationary as inflation goes higher. Therefore, this outcome is not in line with previous studies, which show that the impact of fiscal deficits is stronger when inflation is high.

However, if money growth rates are included in xit−j(refer to the model proposed by Kwon et al., 2009, and many empirical works such as Darrat, 1985, Giannaros and Kolluri, 1986, Karras, 1994, and most papers which employ VAR),¹² the results are ameliorated and shown in Table 9 and the estimates of the deficit-to-GDP ratios

11Data of the deficit-to-GDP ratio is stationary over 1960–2006, and the t-statistic of the Levin-Lin-Chu test (one lag) for the deficit-to-GDP ratio is -25.45.

12Data of the money growth rate is stationary over 1960–2006, and the t-statistic of the Levin-Lin-Chu test (one lag) for money growth is -29.68.

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are plotted on the lower part of Figure 3.¹³ (As inflation, money growth is also transformed into a logarithmic form (log(1+money growth)).) From quantile 0.1 to 0.9, the summations of coefficients of the deficit-to-GDP ratios are 0.1147, 0.1473, 0.1545, 0.1829, 0.1885, 0.2104, 0.2170, 0.2208 and 0.2416. They are significant at the 1% level at quantiles 0.1–0.8 and significant at the 5% level at quantile 0.9.

Although the deficit-to-money ratio is insignificant at quantile 0.1, the summation of coefficients of deficit-to-GDP ratios still becomes larger as the quantile goes higher.

Therefore, when standard specifications (deficit-to-GDP ratio) are estimated, the money growth rates should be controlled. The D-GMM L and D-GMM D estimators are 0.5190 and 0.5372 respectively, and both are significant at the 1% level. These two estimators also support that fiscal deficit is inflationary.

In summary, the dynamic panel results over 1960–2006 show that as inflation rises, the fiscal deficits will be more inflationary, and fiscal deficits will play a weak or non-existing role in inflation when inflation is at a low level. Whether I scale deficits by money, or scale deficits by GDP and control money growth, the results will not change. Therefore, we can know that fiscal consolidation would become more effective in price stabilization as inflation rises.