*3.1. Data Description*

Our model is estimated on U.S. data for two samples, 1954:3–1979:2 (S1) and 1983:1–2008:2 (S2). As we explained above, in the early 1980s, financial liberalisation occurred. Therefore, our choice of splitting the overall sample reflects the hypothesis of a structural break in such a period.

Our choice of ending S2 in 2008:2 is because this period coincides with the beginning of the U.S. financial crisis. As a consequence, the Fed adopted an unconventional monetary policy, which resulted in the short-term nominal interest rate approaching the zero-lower bound. As Christiano et al. (2011) and Ramey and Zubairy (2018) argued, in such a situation, the effects of fiscal spending shocks on several macroeconomic aggregates substantially changed with respect to "normal" times.

As we mentioned above, we have two separate models. In the first model, we assumed that the whole economy was driven by three exogenous shocks: total governmen<sup>t</sup> spending ( *Gt* ), inflation objective ( *<sup>π</sup>* ¯ *t* ) and monetary policy ( *Rt* ). Since there were three exogenous shocks, we used three observed variables to estimate this model: total governmen<sup>t</sup> spending, inflation rate and short-term nominal interest rate. The series of the total governmen<sup>t</sup> spending was taken from the U.S. Bureau of Economic Analysis (BEA). The inflation rate corresponded to the quarterly growth rate of the GDP price index. For the short-term nominal interest rate, we considered the effective federal funds rate expressed in quarterly terms. The source of these two data series was the website of the Federal Reserve Bank of St. Louis.

In the second model, we disaggregated total public spending into non-military and military components. Thus, the exogenous processes governing the economy were four: non-military expenditure ( *NMt* ), military spending ( *Mt* ), inflation objective ( *<sup>π</sup>*¯*t* ) and monetary policy ( *Rt* ). Thus, we used four observed variables to estimate this model: non-military expenditure, military expenditure, inflation rate and short-term nominal interest rate. The data series for non-military and military spending were obtained from the U.S. BEA. In particular, military spending corresponded to national defence data, whereas non-military spending was obtained from the difference between governmen<sup>t</sup> consumption expenditures and gross investment data and national defence data. For inflation rate and short-term nominal interest rate, we used the data series that we mentioned above.

In both models, we deflated all variables using their respective deflators. Moreover, we expressed the several variables in log per capita terms. Finally, we detrended all the series using the Hodrick–Prescott filter with a smoothing parameter equal to 1600.

#### *3.2. Prior Distributions of the Parameters*

We split the parameters of our models into two groups. The first set was kept fixed. The parameters of this group can be viewed as strict priors, and we set their values in line with previous literature (Galí et al. 2007; Bilbiie et al. 2008). The second group of parameters was estimated using the Bayesian method.

Table 1 shows the fixed parameters in the two sub-samples for both the aggregate governmen<sup>t</sup> spending model and the disaggregated model. From Panel (a), we note that the share of governmen<sup>t</sup> expenditure on GDP in S1 was higher than the one in S2. This reflects that fact that the average of public spending decreased over time. Focusing on the disaggregated model, Panel (b) shows that also the shares of non-military spending on GDP (*NMY*) and military spending on GDP (*MY*) decreased from S1 to S2.


**Table 1.** Fixed parameters for both models. S, Sub-sample.

In line with Bilbiie et al. (2008), we kept *φg* equal to 0.17 in S1 and 0.64 in S2 for both the aggregate governmen<sup>t</sup> spending model and the disaggregated expenditure model. This implies that there was a greater reliance on deficits to finance an extra public spending unit in S2 than S1. Following Bilbiie et al. (2008), we fixed *η* equal to 0.51 in the first sub-sample and to 0.71 in the second sub-sample for both the aggregate governmen<sup>t</sup> expenditure model and the disaggregated spending model. Such values imply a greater persistence of deficits in the second sub-sample.

For the remaining fixed parameters, we used the same values for both sub-samples and in both models. The discount factor (*β*) corresponded to 0.99, which implies an annual steady state real interest rate of 4%. Moreover, we assumed that, in the steady state, agents spend one-fourth of their time endowment working. Following Bilbiie et al. (2008), we set the inverse of the intertemporal elasticity of substitution (*σ*) equal to two. The price elasticity of demand for intermediate goods (*ε*) was chosen such that the mark-up in the steady state equalled 20%. Moreover, in line with Del Negro and Schorfheide (2008), we fixed the probability that prices did not change in a given period (*α*) at 0.75. Finally, we set the steady state tax rate (*τ*) equal to 0.3. Together with the assumption that the steady-state share of debt was zero, these last two parameters pinned down lump-sum transfers in the steady state.

Table 2 displays the prior distributions of the endogenous parameters estimated with Bayesian techniques for both models in S1 and S2. We start by describing our prior assumptions on the share of non-asset holders. In line with the findings by Bilbiie et al. (2008), for both models, we assumed that (*λ*) was gamma distributed and had a higher prior mean in S1 than S2.


**Table 2.** Priors of endogenous parameters for both models.

Notes: In the above table, S1 denotes the first sub-sample, whereas S2 indicates the second sub-sample.

Turning to the parameters of the monetary policy rule, we chose a pretty general and agnostic approach by assuming the same prior distributions in both sub-samples and for both models. Our priors were in line with the values found by Smets and Wouters (2007). In particular, we assumed that the interest rate smoothing parameter was beta distributed with prior mean and standard deviation corresponding to 0.65 and 0.10, respectively. The prior for the coefficient on inflation was assumed to have a gamma distribution with mean equal to 1.5 and standard deviation equal to 0.1. Moreover, we assumed that the coefficient on output was gamma distributed with mean equal to 0.10 and standard deviation equal to 0.05.

Table 3 shows the priors of the stochastic processes. The distribution for these parameters was the same in both models and sub-samples. In line with Smets and Wouters (2007), we assumed that the persistence parameters of the *AR*(1) processes were beta distributed with means equal to 0.70 and standard deviations equal to 0.20. Finally, the standard errors of the innovations were assumed to follow inverse-gamma distributions with mean equal to 0.01 and infinite degrees of freedom.


**Table 3.** Priors of shock processes for both models.

Notes: In the above table, S1 denotes the first sub-sample, whereas S2 indicates the second sub-sample.

#### *3.3. Posterior Estimates of the Parameters*

In both models and in both sub-samples, for the group of parameters estimated with the Bayesian method, firstly, we estimated the mode of the posterior distribution by maximising the log posterior function, which combined the priors with the likelihood function given by the data. Secondly, we used the Metropolis–Hastings algorithm to obtain the full posterior distribution.<sup>3</sup> Our samples included 1,000,000 draws, and we dropped the first 250,000 of them. The acceptancerates for the total governmen<sup>t</sup> spending model corresponded to 35% in S1 and 33% in S2, whereas for the model with disaggregated public spending, the components in S1 and S2 were equal to 32% and 33%, respectively. In order to test the stability of the samples, we used the diagnostic test of Brooks and Gelman (1998). We also used other diagnostic tests for our estimates, including the Monte Carlo Markov Chain (MCMC) univariate diagnostics and the multivariate convergence diagnostics. In terms of parameters identification, we performed the test of Iskrev (2010).<sup>4</sup> Such a test shows that all the parameters for both models and in both sub-samples were identifiable in the neighbourhood of our estimates. Finally, we tested for the possibility of the misspecification of our DSGE model. In line with Albonico et al. (2019), we estimated the DSGE-VAR counterparts (in the spirit of Del Negro and Schorfheide 2004) for the models with aggregate governmen<sup>t</sup> spending, as well as disaggregated non-military and military expenditures in both sub-samples. Overall, our results indicated that, in both sub-samples, the benchmark models outperformed the different DSGE-VAR models.<sup>5</sup>

Tables 4 and 5 report the posterior means for the parameters of both models for S1 and S2 with a 90% confidence interval.


**Table 4.** Estimated posteriors of endogenous parameters for both models.

<sup>3</sup> All the estimations were done with Dynare (http://www.dynare.org/).

<sup>4</sup> All the relative figures are reported in Appendix D together with prior and posterior distributions of the parameters estimated with Bayesian methods.

<sup>5</sup> In Appendix F, Tables A1 and A2 compare the different DSGE-VAR models against the benchmark models, reporting their marginal log densities and Bayes factors.


**Table 5.** Estimated posteriors of shock processes for both models.

We start by describing the estimates of the share of non-asset holders (*λ*). From Table 4, we observe that asset market participation differed considerably across periods. More specifically, for the model with aggregate governmen<sup>t</sup> spending, the share of consumers who did not smooth consumption by trading in assets was estimated as 0.45 in S1 and as 0.29 in S2. Similar values were found for the model with disaggregated public spending components. These results imply that access to asset markets widened with the important institutional changes in the early 1980s. As we will discuss below, this result had important implications for the several fiscal policy shocks.

Focusing on the estimated parameters for monetary policy, we note that for the model with aggregate governmen<sup>t</sup> spending in both sub-samples, the nominal interest responded more strongly to inflation than output changes. Our finding was in line with Andrés et al. (2009). Interestingly, we found that the interest smoothing parameter had a larger value in S2 than S1. The estimates for these parameters showed a similar value for the model with disaggregated governmen<sup>t</sup> spending.

A number of observations are worth making regarding the estimated exogenous processes. In the model with aggregate governmen<sup>t</sup> spending, we found that the expenditure shock volatility (*<sup>σ</sup>G*) was much larger in S1 than S2. Similarly, governmen<sup>t</sup> spending shocks were more persistent in S1 than S2. Regarding the shocks to monetary policy, the inflation target shock was more volatile in S2 than S1, whereas the nominal interest rate shock had a higher volatility in the first sub-sample. Such results confirm a stronger central bank response to inflation in the second sub-period.

Focusing on the model with non-military and military expenditures, we noted remarkable differences across the two sub-samples and between the two components. Firstly, we noted that the volatilities of the governmen<sup>t</sup> spending components were larger in the first sub-sample. Secondly, we found that civilian spending shocks were more persistent in S2, whereas the opposite occurred to military expenditure shocks. Thirdly, our results showed that *σM* was almost double of *σNM* in both S1 and S2. Such findings confirmed that military spending shocks were much more volatile than civilian shocks. Similarly, military expenditure shocks were more persistent than civilian spending shocks in both sub-samples.

#### **4. Analysing the Effects of Different Public Spending Shocks on the Economy**

In this section, we show the impulse responses by assuming a 1% increase in total government, civilian and military expenditures. More specifically, we set the values of the several parameters equal

to their mean estimates of their posterior distributions. This strategy allowed us to compare the effects of several public spending shocks on the economy effectively.<sup>6</sup>

#### *4.1. Model with Aggregate Government Spending*

Figure 1 plots the impulse responses to a positive governmen<sup>t</sup> spending shock. We observed that such a shock was more persistent in the first sub-sample. This result was in line with the studies by Fatás and Mihov (2003) and Perotti (2005).

**Figure 1.** Total governmen<sup>t</sup> spending shock. Notes: Simulated 1% increase in total governmen<sup>t</sup> spending. Parameters are set according to their estimated values. The blue lines indicate the responses of the estimated model for S1, whereas the red lines denote the responses of the estimated model in S2.

Our results indicate that, on the shock impact, output increased by 0.15% in S1 and 0.16% in S2. However, from the fourth quarter onwards, we noted a smaller increase in GDP during the post-financial liberalisation period than in S1. Our findings were in line with Albonico et al. (2017), who found that in recent years, and especially during the Great Recession, the discretionary fiscal stimulus has played a negligible role in stabilising the U.S. economy.

From Figure 1, we note that, in both sub-samples, an increase in governmen<sup>t</sup> spending induced an increase in hours worked. This occurred because both non-asset and asset holders increased their labour supply due to the negative wealth effect induced by the increase in taxation. Aggregate wages fell in response to the shock because the shift in labour supply dominated the shift in labour demand.

Moreover, the nominal interest rate increased. As a consequence, private consumption decreased. Such a finding confirmed the predictions of standard neoclassical models in which higher governmen<sup>t</sup> spending tends to depress the consumption of asset holders. The reason was the negative wealth effect resulting from the induced increase in the tax burden. Such an effect was strengthened by the increase

<sup>6</sup> In Appendix E, we report the estimated IRFs and their relative error bands for all three public spending shocks in both sub-samples.

in the nominal interest rate. A more aggressive monetary policy implies a higher real interest rate and, in turn, lowered the incentive of asset holders to postpone consumption.

Interestingly, we found that private consumption had a larger fall in S1 than S2. This is explained by the higher persistence of the governmen<sup>t</sup> spending shock in the first sub-sample that increased the present discounted value of taxes and the wealth effect on asset holders.

#### *4.2. Model with Non-Military and Military Expenditures*

Figures 2 and 3 show the impulse responses to non-military and military spending shocks, respectively.

We start by describing the effects of a 1% increase in non-military spending (Figure 2). We observed that the persistence of the shock was much lower in S1 than S2. Moreover, our results showed that, on impact, output increased by 0.13% in the first sub-sample and by 0.10% in the second sub-sample. Similarly, hours worked increased in both S1 and S2.

**Figure 2.** Non-military spending shock. Notes: Simulated 1% increase in non-military spending. Parameters are set according to their estimated values. The blue lines indicate the responses of the estimated model for S1, whereas the red lines denote the responses of the estimated model in S2.

Interestingly, we noted that the responses of aggregate wage and private consumption were very different across the two sub-samples. In particular, we observed an increase in these two variables in S1, whereas they both fell in S2. Therefore, our results showed the crowding-in effect before the 1980s and the crowding-out effect thereafter. The reason for the crowding-in effect in S1 was the strong enough rise in the real wage. Such an increase induced a rise in the consumption of non-asset holders, which more than offset the fall in consumption of asset holders. The increase in the aggregate wage crucially depended on the interaction between labour demand and supply. On the one hand, a positive civilian spending shock increased the demand for goods and, in turn, affected labour demand. The firms that could not change their prices and had to adjust their quantities hence shifted labour demand at a given wage. On the other hand, labour supply shifted for two different reasons. Firstly, non-asset holders would work more as tax burden increased. Secondly, asset holders also increased labour supply for a given wage: this was due both to the wealth effect and to intertemporal substitution.

The lower persistence of the civilian spending shock in S1 implied a lower wealth effect on asset holders, and in turn, the shift in labour demand dominated the shift in labour supply. Accordingly, the real wage increased enough to raise aggregate consumption. Since the opposite effects occurred in the second sub-sample, we observed crowding-out on private consumption. Finally, we note that the nominal interest rate increased more in the first sub-sample, weakening the positive effect of the civilian spending shock on consumption.

We now turn to the effects of a 1% increase in military spending. As we can observe in Figure 3, the persistence of this shock was higher in S1 than S2. Interestingly, we note that the positive effect on output implied by these shocks was lower compared to the increased civilian spending for both sub-samples (0.04% in S1 and 0.05% in S2).

**Figure 3.** Military spending shock. Notes: Simulated 1% increase in military spending. Parameters are set according to their estimated values. The blue lines indicate the responses of the estimated model for S1, whereas the red lines denote the responses of the estimated model in S2.

Moreover, it is possible to observe that in both S1 and S2, hours worked increased in response to the shock due to the negative wealth effect associated with the increase in taxation. Our results indicated a larger fall in the aggregate wage during the first sub-sample. As a consequence, private consumption dropped more substantially in S1 than S2.

From these results, it is evident that there were important differences between the effects of civilian and military spending. In the pre-1980 period, an increase in civilian expenditure induced a crowding-in effect on private consumption for the U.S. economy. On the contrary, military spending shocks caused a systematic fall in private consumption. Moreover, we note that the civilian spending had a more positive impact on output than military expenditure for both sub-samples.<sup>7</sup>

#### **5. Robustness Analysis: Different Assumptions about the Taylor Rule**

In this section, we investigate the role of monetary policy in the presence of the shocks to total government, non-military and military spending. In particular, we provide a counterfactual analysis in which the central bank has a more aggressive monetary policy. More specifically, we assumed that in the Taylor rule (21), the parameters measuring the response of the policy rate to output (*ry*) and inflation (*<sup>r</sup>π*), as well as the interest rate smoothing parameter (*ρ<sup>R</sup>*) assumed values that were double those estimated by our models.

Figure 4 shows the responses for both output and consumption in the case of an increase in total government, non-military and military spending, respectively. The black lines represent the responses of output and consumption in the presence of the actual monetary policy, whereas the green lines show the IRFs for the same variables in the presence of a more aggressive monetary policy.

As we explained in the previous section, a more aggressive monetary policy implies a higher nominal interest rate that strengthened household incentives to postpone consumption. As a consequence, private consumption and output were lower. In fact, the top panels of Figure 4 show that in the case of total governmen<sup>t</sup> spending, for the first sub-sample, both output and consumption were lower in the presence of a more aggressive monetary policy (on the shock impact, 0.01% lower than in the benchmark case). In the second sub-sample, the same effects with similar magnitudes can be observed.

The mid panels of Figure 4 show a more striking difference in the responses of consumption and output to an increase in non-military spending. In S1, although in the presence of the actual monetary policy, private consumption increased, when a more aggressive monetary policy was in operation, the crowding-out effect emerged. In turn, this implies that output in the counterfactual scenario was lower than in the actual case by 0.02%. These effects are less pronounced in the second sub-sample. Finally, the bottom panels of Figure 4 show that different monetary policies had negligible effects in the case of an increase in military spending.

<sup>7</sup> In order to further assess the different contribution of fiscal spending shocks on aggregate output, we also performed the forecast error variance decomposition for 1, 4, 10, and 30 quarters ahead (Albonico et al. 2019). Our results indicated that fiscal spending shocks had larger contributions on GDP during the post-financial liberalisation period. Moreover, we found that non-military spending shocks contributed to output changes more than military spending shocks.

Total Government Spending Shock

**Figure 4.** Alternative assumptions on the Taylor rule. Notes: In the above graphs, the black lines denote the IRFsin the presence of the actual U.S. monetary policy, whereas the green lines indicate the IRFs associated with the counterfactual monetary policy.
