3.1. Data

The data used in our analysis are sourced from the OECD’s Statistics and Projections Database, OECD Economic Outlook, and the International Monetary Fund’s World Economic Outlook. Macroeconomic series, such as real GDP, real consumption, real investment, and employment, are obtained from the OECD Economic Outlook. The debt-to-GDP ratio is sourced from the International Monetary Fund’s World Economic Outlook. In addition, the data on the consumer confidence index and business confidence index are collected from the OECD database. For the forecast of government spending, we use the forecast reported in the fall issue of the OECD Economic Outlook for the same year to construct government spending shocks.Footnote ⁶ The old-age dependency ratio is obtained from the World Bank’s World Development Indicator. It is defined as the ratio of the population aged over 65 years to the population aged 15–64 years.Footnote ⁷ Our sample includes an unbalanced panel of 24 OECD countries for the period 1985–2019. Our analysis uses the old-age dependency ratio as a measure of the aging state of an economy. We define an economy as aged when the old-age dependency ratio exceeds a certain threshold. In our analysis, an economy is regarded as aged (nonaged) if its old-age dependency ratio is above (below) the sample mean of 22.8%.Footnote ⁸ After dividing 24 OECD countries into aged and nonaged economies, we estimate state-dependent local projections using the debt-to-GDP ratio as a transition variable that drives the dynamics of the fiscal multipliers in each group of countries.

It is worth noting that there are two issues for the selection of countries in each group. The first issue is associated with consistency in assigning countries in each group. Among aged economies, Japan exhibited remarkable changes in the demographic structure over our sample period 1985–2019. While Japan was included in the nonaged group in the early stage of our sample period, it became the most aged economy in the aged group in a short period of time.Footnote ⁹ Similarly, the Netherlands was undoubtedly included in the nonaged group until 2010. However, after 2010, it was included in the aged group with the old-age dependency ratio sharply increasing from 23.03 in 2010 to 30.39 in 2019. To address the issue of consistency in assigning countries in each group, we estimate the model using aged economies without Japan and nonaged economies without the Netherlands and discuss the results accordingly in Section 4.2.

Another issue would be discrepancy of the government debt level between the two groups since there is a positive correlation between government debt and population aging. While the median for the government debt-to-GDP ratio is 60.52 for the aged group, it is 55.06 for the nonaged group. If the government debt-to-GDP ratio substantially differs across the two groups, it appears to be difficult to distinguish between the effects of population aging and those of government debt.Footnote ¹⁰ To investigate how robust our main findings are to the issue of discrepancy, we estimate the model with some adjustments for this discrepancy, i.e., by excluding one country with an extreme outlier for the debt level in each group: Japan exhibiting the highest debt level in the aged group and Luxemburg showing the lowest debt level in the nonaged group. Making adjustments for this discrepancy provides quite similar median values of the government debt-to-GDP ratio for aged and nonaged groups. Specifically, the median for the aged group becomes 59.06 and for the nonaged group, 60.46.Footnote ¹¹

3.2. Identification of government spending shocks

Following the Auerbach and Gorodnichenko (Reference Auerbach and Gorodnichenko2012, Reference Auerbach, Gorodnichenko, Auerbach and Gorodnichenko2013)’s approach, we identify government spending shocks as forecast errors of government spending. Specifically, government spending shocks are identified as follows:

\begin{equation*} \varepsilon _{it}=\frac {G_{it}-G_{it}^{e}}{Y_{i,t-1}}, \end{equation*}

where $G_{it}$ is the actual government consumption of country $i$ in year $t$ , $G_{it}^{e}$ is the forecast of government consumption spending, and $Y_{i,t-1}$ is real GDP of country $i$ in year $t-1$ . We use forecasts from the fall issue of the OECD Economic Outlook and data sourced from the OECD’s Statistics and Projections Database. Specifically, to obtain government spending shocks, we use the forecast of government spending in the fall issue of the OECD Economic Outlook for the same year. We also use the forecast of government spending in the fall issue of the previous year as a robustness check. This identification strategy could resolve the well-known issues of (i) fiscal foresight [Leeper et al. (Reference Leeper, Richter and Walker2012, Reference Leeper, Walker and Yang2013)] and (ii) potential feedback from the state of the economy to fiscal policy. We scale fiscal variables (i.e., $G_{it}$ and $G_{it}^{e}$ ) by real GDP in the previous year, so that the estimated coefficients are fiscal multipliers.Footnote ¹²

Based on the available data regarding forecast errors of government spending, our sample covers the following countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the USA.

3.3. Model estimation using local projections

As in Auerbach and Gorodnichenko (Reference Auerbach and Gorodnichenko2012, Reference Auerbach, Gorodnichenko, Auerbach and Gorodnichenko2013), we estimate nonlinear (or state-dependent) local projections to quantify the effects of government spending shocks on macroeconomic variables such as output, private consumption, investment, and employment by using heterogeneous panel data for 24 OECD countries in the sample. Local projections are found to have some distinct advantages compared to VAR models: (i) local projections are more robust to misspecification since they impose weaker assumptions on the dynamics of the data; (ii) a joint or point-wise analytic inference is readily implemented; and (iii) compared to VAR models, local projections are easier to estimate. However, there is one drawback in using local projections—chiefly, the importance of identifying structural shocks beforehand. Thus, we use the government spending shock identified as explained above in the estimation of nonlinear local projections.

We estimate the following state-dependent local projection model.

(1) \begin{equation} y_{i,t+h}-y_{i,t-1}=\alpha _{i}^{h}+\theta _{t}^{h}+\beta _{1}^{h}G\left ( z_{it}\right ) \varepsilon _{it}+\beta _{2}^{h}\left [ 1-G\left ( z_{it}\right ) \right ] \varepsilon _{it}+\omega ^{h}X_{it}+u_{i,t+h}^{h}, \end{equation}

with

\begin{equation*} G\left ( z_{it}\right ) =\frac {\exp \left ( -\gamma z_{it}\right ) }{1+\exp \left ( -\gamma z_{it}\right ) },{ \,}\gamma \gt 0 \end{equation*}

where $y_{i,t}$ is the log of real GDP, $\alpha _{i}^{h}$ is the country fixed effect, $\theta _{t}^{h}$ is the time fixed effect, $\varepsilon _{it}$ is the identified government spending shock, and $X_{it}$ is a set of control variables. The control variables include two lags of government spending shocks and two lags of real GDP growth. All the coefficients vary with horizon $h$ . Thus, equation (1) is estimated separately for each horizon. We estimate equation (1) for each $h=0,1,\ldots,4$ , where $h=0$ indicates the year in which the government spending shock occurs. We compute the impulse response function of output using the estimated $\beta ^{h}$ . We set $\gamma =1$ as in Abiad et al. (Reference Abiad, Furceri and Topalova2016) and Miyamoto and Yoshino (Reference Miyamoto and Yoshino2022).Footnote ¹³ The transition variable $z$ is the government debt-to-GDP ratio. As in Auerbach and Gorodnichenko (Reference Auerbach and Gorodnichenko2012), we date the transition variable $z$ by $t-1$ to avoid contemporaneous feedbacks from policy actions as to whether the economy is in a high- or a low-debt regime.Footnote ¹⁴ Standard errors are obtained using the robust covariance matrix estimator of Driscoll and Kraay (Reference Driscoll and Kraay1998). The estimation results remain consistent in the presence of cross-sectional dependence and serial correlation and thus provides heteroskedasticity-robust standard errors.

4.1. Results from state-dependent local projections

Figure 3 illustrates the cumulative impulse responses to an unanticipated increase in government spending by 1% of GDP at time 0 for all of our sample economies (i.e., unconditional on population aging). The shaded area represents 90% confidence bands. At first glance, impulse responses qualitatively confirm the findings of previous studies. That is, fiscal stimulus based on government spending increases is effective when the government debt level is low and ineffective when it is high. In the high-debt regime, the impact multiplier is estimated to be –1.3, and the cumulative magnitude falls to –3 in Year 4. In contrast, in the low-debt regime, the impact multiplier is estimated to be 2, and the cumulative multiplier rises to 5.4 in Year 4.

Figure 3. State-dependent impulse responses of output to an unanticipated government spending shock for 24 countries in the sample, with 90% confidence bands.

In previous studies, the fiscal multiplier, depending on the government debt level, is estimated to varying degrees, which stems from different sample countries, sample periods, and estimation methodologies. In the high-debt regime, Ilzetzki et al. (Reference Ilzetzki, Mendoza and Végh2013) and Nickel and Tudyka (Reference Nickel and Tudyka2014) find significantly negative fiscal multipliers, whereas Koh (Reference Koh2017) and Huidrom et al. (Reference Huidrom, Kose, Lim and Ohnsorge2020) find insignificant output effects. Ilzetzki et al. (Reference Ilzetzki, Mendoza and Végh2013) provide a similar long-run multiplier to our case, which is –3, when the government debt-to-GDP ratio exceeds 60%, but the multiplier is nil when it remains lower. Nickel and Tudyka (Reference Nickel and Tudyka2014) report that the estimated impact multiplier is 1.2; however, the persistence of the positive effect is eroded as the debt-to-GDP ratio increases, and there are significantly negative output effects in the long run when the ratio exceeds 109%. Koh (Reference Koh2017) shows that the long-run multiplier is still significant and positive at approximately 0.4 when the government debt-to-GDP ratio exceeds 60%, but they also find that it becomes close to zero when it exceeds 90%. Lastly, Huidrom et al. (Reference Huidrom, Kose, Lim and Ohnsorge2020) estimate that the 2-year multiplier is 0.6 when the government debt is below 17% of GDP, while it is insignificant when it is above 92% of GDP. The impulse responses depicted in Figure 3 appear to be consistent with those of Ilzetzki et al. (Reference Ilzetzki, Mendoza and Végh2013) and Nickel and Tudyka (Reference Nickel and Tudyka2014) in that the significantly negative multiplier is pronounced in the high-debt regime, while a significant and positive multiplier is evident in the low-debt regime.

As explained above, the impulse responses in Figure 3 have already been reported in existing literature. However, in our study, we consider the fact that population aging is correlated with the government debt level. To separate these two effects, we divide our sample economies into the two groups, “aged and nonaged,” based on the mean of the old-age dependency ratio. Figure 4 plots state-dependent impulse responses depending on the government debt-to-GDP ratio for both the aged and nonaged groups. We also report the p-values for state-dependent impulse responses in Table 1. First, in the upper panels of Figure 4, for aged economies, fiscal stimulus is found to be ineffective, regardless of the government debt level. That is, the output responses to a government spending shock are not significant. Honda and Miyamoto (Reference Honda and Miyamoto2021) and Miyamoto and Yoshino (Reference Miyamoto and Yoshino2022) also find that the output effects of fiscal policy are insignificant in aged economies. However, distinct from the previous studies, Figure 4 indicates that the effect of population aging on the fiscal multiplier prevails irrespective of the level of government debt.

Figure 4. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

Table 1. State-dependent impulse responses of various variables to an unanticipated government spending shock

Notes. In panels (a)–(d), the state-dependent impulse responses of macroeconomic variables to an unanticipated government spending shock are reported. In panels (e) and (f), state-dependent impulse responses of CCI and BCI to an unanticipated government spending shock are reported, respectively, as further analysis. The p-value is in brackets below the corresponding estimate. $^{*}$ , $^{**}$ , and $^{***}$ indicate 10%, 5%, and 1% statistical significance, respectively.

In contrast, for nonaged economies, the level of government debt may govern the output effect of fiscal policy. The lower panels of Figure 4 show that a positive government spending shock lowers output for nonaged economies with high-debt levels, whereas it increases output for nonaged economies with low-debt levels. The impulse responses are consistent with those of Ilzetzki et al. (Reference Ilzetzki, Mendoza and Végh2013) and Nickel and Tudyka (Reference Nickel and Tudyka2014), in that expansionary fiscal policy is contractionary in countries with high government debt. However, Figure 4 indicates that the contractionary output effect is at work only in nonaged economies. Furthermore, expansionary fiscal policies can stimulate the economy only for nonaged economies with a low government debt level. It is also worth noting that the magnitude of the impulse responses for nonaged economies in Figure 4 is greater than that of our baseline case (i.e., unconditional on population aging) in Figure 3. Specifically, for nonaged economies, the impact multiplier is –2 in the high-debt regime and 3.1 in the low-debt regime (compared to –1.3 in the high-debt regime and 2 in the low-debt regime when population aging is not considered).

The main findings from Figures 3 and 4 suggest that a demographic structure plays a key role in determining the fiscal multiplier, irrespective of the level of government debt.Footnote ¹⁵ Thus, further investigation of each route, through which population aging and government debt affect the fiscal multiplier, is necessary. Figures 5, 6, and 7 along with Table 1 show the impact of a government spending shock on private consumption, private investment, and employment, respectively. The impulse responses for aged economies in Figures 5 and 6 indicate that consumption and investment do not increase at the initial stage, even in the low-debt regime, which prevents the output effect of fiscal expansion. Similarly, there is also no crowding-out effect in the high-debt regime for nonaged economies in Figures 5 and 6. For aged economies, fiscal surprises cannot influence consumption and investment and, therefore, have no effect on output. However, for nonaged economies, as shown in Figures 5 and 6, consumption and investment fall in response to government spending expansion in the high-debt regime, while they significantly rise in the low-debt regime.

Figure 5. State-dependent impulse responses of private consumption to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

Figure 6. State-dependent impulse responses of investment to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

Figure 7. State-dependent impulse responses of employment to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

As pointed out by Yoshino and Miyamoto (Reference Yoshino and Miyamoto2017), this sharp contrast can be accounted for by the sluggish response of the labor market in an aged economy. They show that fiscal multipliers are smaller in an aged economy since the employment effects of the policy are limited because the larger proportion of retired people in an aged economy. Furthermore, Bachmann and Sims (Reference Bachmann and Sims2012) show that markets’ confidence regarding the future economy is the main route for determining fiscal multipliers; furthermore, the results of Rendahl (Reference Rendahl2016) indicate that an increase in employment would help market participants increase their confidence in the future economy. Therefore, employment may be a key channel for understanding the responses of consumption, investment, and output.Footnote ¹⁶

In Figure 7, for aged economies, employment does not fall in response to a fiscal expansion in the high-debt regime and does not rise in the low-debt regime. On the contrary, for nonaged economies, employment shrinks in response to fiscal expansion in the high-debt regime, which leads to a crowding-out of consumption and investment, and in turn, output falls due to this crowding-out effect. However, in the low-debt regime, employment increases significantly in response to expansionary fiscal shocks, which boosts consumption and investment and, in turn, output increases. The responses of employment are consistent with those of consumption, investment, and output.

4.2. Robustness checks

In this section, we check the robustness of our empirical results for state-dependent local projections.Footnote ¹⁷ First, we obtain impulse responses with additional control variables such as lagged short-term interest rates and tax revenues. Figure 8 displays impulse responses of output to a government spending shock with additional lagged control variables. For both aged and nonaged economies, the results are quite similar to those from the baseline case, as reported in Figure 4.Footnote ¹⁸ Figure 9 shows impulse responses for aged and nonaged groups, using data excluding Japan and the Netherlands, respectively. As discussed in Section 3.1, Japan and the Netherlands are considered to be exceptional cases, featuring rapidly growing population aging: while both economies exhibited a relatively young demographic structure in the early stage of the sample period, they were classified as aged economies in the later sample period. Figure 9 confirms that our key findings in Figure 4 remain qualitatively unaltered. That is, the responses of output are broadly insignificant in aged economies; while there are negative effects on output in nonaged and high-debt economies, there are positive effects on output in nonaged and low-debt economies. In addition, it is worth mentioning that the responses of output to a government spending shock in the nonaged group are greater than those in the baseline case of Figure 4.

Figure 8. Robustness check. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands. Lagged short-term interest rates and tax revenues are included as additional control variables.

Figure 9. Robustness check. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands. To address the issue associated with consistency in assigning countries in each group, we exclude Japan in aged economies and the Netherlands in nonaged economies since two countries moved from one group to another during our sample period.

We also use an alternative government spending shock. That is, a government spending shock is generated using the forecast of government spending in the fall issue of the previous year rather than the same year as in the baseline case. Figure 10 depicts the state-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies with 90% confidence bands. For aged economies, fiscal policy is ineffective regardless of the level of government debt. For nonaged economies, while fiscal policy leads to negative effects on output up to 1 year in times of high debt, its positive effects on output are more pronounced in times of low debt and last for about a year. Thus, the estimated impulse responses exhibit a qualitatively similar pattern for aged and nonaged economies compared with the baseline case, thus confirming our main hypothesis that fiscal multipliers are state contingent.

Figure 10. Robustness check. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands. The government spending shock is generated using the forecast of government spending in the fall issue of the previous year.

Furthermore, to mitigate the endogeneity problem caused by unanticipated business cycle conditions, local projections are estimated with additional control variables, such as current and lagged output growth shocks, which are defined as the forecast error of GDP growth. Figure 11 depicts the state-dependent impulse responses of output to an unanticipated government spending shock, including current and lagged output growth shocks as additional control variables, in both aged and nonaged economies with 90% confidence bands. This clearly shows that considering an unanticipated business cycle condition generates qualitatively similar results to the baseline case. That is, in aged economies, fiscal policy is ineffective regardless of the level of government debt. However, in nonaged economies, while fiscal policy leads to negative effects on output in times of high debt, its positive effects are more pronounced in times of low debt.

Figure 11. Robustness check. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands. Local projections are estimated with additional control variables such as current and lagged output growth shocks, which are defined as the forecast error of the GDP growth rate, to mitigate the endogeneity problem caused by an unanticipated business cycle condition.

Since a high old-age dependency ratio implies labor scarcity which could be a driving force behind our results, we have also included the measure for labor market tightness in the estimation. As in Duval et al. (Reference Duval, Ji, Li, Oikonomou, Pizzinelli, Shibata, Sozzi and Tavares2022), we employ the ratio of open vacancies to the number of unemployed (i.e., the vacancy-to-unemployment ratio) as a measure for labor market tightness. That is, local projections are estimated with additional control variables, including the current and lagged vacancy-to-unemployment ratio, which is obtained from the IFS and OECD database. Figure 12 depicts the state-dependent impulse responses of output to an unanticipated government spending shock, including the current and lagged measure for labor market tightness as additional control variables, in both aged and nonaged economies with 90% confidence bands. This indicates that considering tightness in the labor market provides qualitatively similar results to the baseline case.

Figure 12. Robustness check. State-dependent impulse responses of output to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands. Local projections are estimated with additional control variables including the current and lagged measure for labor market tightness.

Furthermore, we implement various robustness checks.Footnote ¹⁹ We use different lags of control variables (1, 3, and 4), such as government spending shocks and real GDP growth, in estimating state-dependent local projections. The results obtained using different lags are similar to our baseline results. We also obtained the results by excluding outliers that could influence our main results. The estimation results confirm that our main results remain qualitatively unaltered. We divide the 24 OECD countries into aged and nonaged economies using the sample median for the old-age dependency ratio. The estimation results obtained using the new grouping of countries remain qualitatively similar. All the results from the robustness checks are similar to the baseline results, as shown in Figure 4.

4.3. Discussion

We discuss the fiscal transmission mechanism of government spending shocks. Figures 13 and 14, combined with Figures 5, 6, and 7, provide supporting evidence for the transmission mechanism as discussed above. Figures 13 and 14 along with Table 1 illustrate the impulse responses of consumer and business confidence, respectively, to the impact of a positive fiscal shock.Footnote ²⁰ Generally, consumer confidence is not significantly affected by fiscal shocks. However, Figure 14 indicates that the responses of business confidence are consistent with those of consumption, investment, and output. While the responses of business confidence are insignificant in aged economies, they are positive in nonaged economies with lower government debt and negative in nonaged economies with higher government debt. Thus, Figure 13 appears to complete the linkage between fiscal policy, employment, and output effects in aged economies: a positive fiscal shock cannot increase employment, which does not enhance business confidence. Stagnated business confidence cannot increase consumption and investment, which results in a lower fiscal multiplier.

Figure 13. State-dependent impulse responses of consumer confidence to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

Figure 14. State-dependent impulse responses of business confidence to an unanticipated government spending shock in both aged and nonaged economies, with 90% confidence bands.

The apparent distinction in employment responses between the aged and nonaged groups can be attributed to the fact that the working-age population is relatively small for aged economies, and therefore, the number of people who can be newly employed by the government’s additional fiscal expansion is also small. In this respect, it is worth focusing on the discussions of Bachmann and Sims (Reference Bachmann and Sims2012) and Rendahl (Reference Rendahl2016). Bachmann and Sims (Reference Bachmann and Sims2012) investigate the role of private agents’ confidence in the economy in determining the output effects of fiscal policy and reveal that, during an economic downturn, the government’s fiscal expansion could have a greater output effect, as it strengthens households’ confidence. Rendahl (Reference Rendahl2016) develops the idea of Bachmann and Sims (Reference Bachmann and Sims2012) by showing that employment is the route through which fiscal expansion increases private confidence and, in turn, output. He argues that the creation of jobs implies a persistent rise in income for private agents, which increases confidence in the future economy and leads to a rise in consumption and investment, resulting in a high fiscal multiplier.

In the context of Bachmann and Sims (Reference Bachmann and Sims2012) and Rendahl (Reference Rendahl2016), for an aged economy, an increase in government spending does not sufficiently raise employment, which does not enhance the economic agents’ confidence in the future economy, thus preventing increases in consumption and investment. Finally, the output effect becomes insignificant. In contrast, for nonaged economies, employment can be significantly affected by fiscal shocks and also rises or falls according to consumption and investment levels. For nonaged economies with high-debt levels, private agents decrease consumption and investment based on expectations of tax increases in the near future, and firms reduce employment in response to lower demand. A fall in employment tends to amplify negative output effects through a vicious cycle that raises pessimistic confidence of the private sector in the economy and reduces private demand. Finally, for nonaged economies with low-debt levels, households increase their consumption, and firms hire more workers, which, in turn, strengthens optimistic confidence in the economy, thus amplifying positive output effects.