2.1 Shock identification and evidence from aggregate data

We identify fiscal policy shocks based on a medium-scale Bayesian SVAR. The identification strategy is inspired by recent work by Baumeister and Hamilton (Reference Baumeister and Hamilton2015), Baumeister and Hamilton (Reference Baumeister and Hamilton2018), and Baumeister and Hamilton (Reference Baumeister and Hamilton2019). It consolidates all known knowledge about the elasticities and IRFs of the model, including their signs and boundaries.

One of the main reasons for going for a VAR-based identification is that many of the other workhorse models used for identifying fiscal shocks require data that is not readily available for the case of China. Especially for the US, there is a large body of literature using military spending, which is believed not to respond to business cycle fluctuations automatically (Burnside et al., Reference Burnside, Eichenbaum and Fisher2004; Hall, Reference Hall2009; Barro and Redlick, Reference Barro and Redlick2011). Others rely on detailed analysis of the institutional setup to identify specific exogenous events (Blanchard and Perotti, Reference Blanchard and Perotti2002) or construct narrative indicators (Romer and Romer, Reference Romer and Romer2010; Ramey, Reference Ramey2011).

Unlike in other VAR literature, where especially the early literature was dominated by (block) recursive identification schemes, the literature on fiscal policy largely uses more theory-based structural restrictions (for a summary, see Ramey (Reference Ramey2016)). The two dominant approaches are zero restrictions on the (semi-)elasticities of the structural equations (see, e.g., Blanchard and Perotti, Reference Blanchard and Perotti2002) and sign restrictions on the impulse response (see, e.g., Mountford and Uhlig, Reference Mountford and Uhlig2009). In more technical terms, given a VAR model of the form $A Y_{t}=B X_{t-1}+\epsilon _{t}$ (where $Y$ is the vector of variables of interest), this corresponds to restrictions on $A$ (elasticities) or $A^{-1}$ (sign restrictions). Baumeister and Hamilton (Reference Baumeister and Hamilton2019) point out two key problems in the most commonly used restrictions. First, for frequentist SVARs imposing restrictions on $A$ , in Bayesian terms, this corresponds to extremely strong prior beliefs on some elements, but completely uninformative priors for others, possibly causing implausible results. Second, they argue that SVARs imposing supposedly uninformative priors for sign restrictions (i.e., only the sign of the response itself is enforced), implicitly impose highly informative and often implausible priors on the elasticities without acknowledging it. Therefore, sign restrictions on IRFs can generate posterior distributions for elasticities that are not consistent with empirical facts.

Since Bayesian SVARs with the type of restrictions and priors we are looking to implement are computationally fairly intensive, we opt for the smallest scale VAR that is feasible to answer our question. Besides government revenue and expenditure and the two investment aggregates we are interested in (non-SOE and SOE investment), we only include real GDP and money. GDP is the main macroeconomic aggregate and a crucial driver of both government spending and revenue. We include money to account for the special Chinese case, where monetary and fiscal policy are highly coordinated. For example, in the aftermath of the Asian financial crisis, the inflation rate became negative during 1998–2000. The monetary policy continued being tough, aiming at imposing hard budget constraints on SOEs, and the fiscal spending was increased at the same time, which stimulated the economy. Therefore, to avoid misinterpreting monetary policy shocks as fiscal, we need to identify a monetary policy shock. As shown by Chen et al. (Reference Chen, Ren and Zha2018), despite China slowly shifting to interest rate-based policies, the quantity of money remains the best measure of policy for our sample.

The VAR thus takes the form

(1) \begin{equation} AY_{t}=B X_{t-1}+\epsilon _{t}, \end{equation}

where $Y$ is a vector of GDP ( $y$ ), government revenue ( $\tau$ ), government spending ( $g$ ), money ( $m$ ), SOE investment ( $is$ ), and non-SOE investment ( $ip$ ), all in log differences, and except M2 all in real per capita terms. We have $X_{t-1}'=(y_{t-1}',y_{t-2}'\ldots .,y_{t-m}',1)$ . The elasticities are collected in $A$ and the parameters guiding the model dynamics in $B$ . $\epsilon _{t}$ is the vector of i.i.d. structural shocks where $\epsilon _{t}\sim N(0,D)$ , and $D$ is a diagonal matrix. The ordering of variables does not affect our identification strategy and is based solely on the relevance of the indicators to ensure a clear and intuitive presentation of the results.

We identify shocks through a combination of zero restrictions on $A$ and informative priors on the remaining elasticities and $A^{-1}$ , i.e., the initial impulse response. While we impose some binding sign restrictions on the elasticities, we have highly informative priors but no binding restrictions regarding the key signs of the impulse response. Following Baumeister and Hamilton (Reference Baumeister and Hamilton2019), we use a t-distribution with three degrees of freedom for the priors of elements in A. If the elasticity has a restriction to be positive or negative, the distribution is truncated accordingly.

The two key equations we are interested in are a fiscal policy rule, which links the budget deficit to the economy, and a revenue equation primarily describing the automatic stabilizer. Those are hit by two shocks, a stimulus shock, which is an unexpected increase in the deficit that might contemporaneously also affect the revenue negatively (i.e., the stimulus might be given through tax credit rather than debt finance spending), and a government size shock, which is an increase in revenue and spending, i.e., a shock on revenue that does not affect the deficit. We model those through informative priors on the sign of the (contemporaneous) impulse response. There is no perfect matching of the more commonly used spending and revenue shocks on the one hand and stimulus and government size shocks on the other hand because our shocks do not affect revenue or taxes exclusively.Footnote ⁴ There is some similarity to debt-financed and tax-financed spending shocks (which are computed as a linear combination of pure spending and revenue shocks) as discussed in Caldara and Kamps (Reference Caldara and Kamps2008). However, contrary to their approach, our stimulus shocks might be driven by tax cuts or credits rather than increased spending.

This yields a fiscal policy rule:

(2) \begin{equation} g_t - \tau _t = \alpha _{g,y} y_t + \alpha _{g,is} is_t + \alpha _{g,ip} ip_t + \varepsilon _{gt}, \end{equation}

where $\alpha _{g,y}$ is expected to be negative (i.e., the deficit increases in a recession) either due to increasing spending or tax cuts, and the prior densities for $\alpha _{g,is}$ and $\alpha _{g,ip}$ are centered around $0$ , since ex-ante we expect fiscal policy to respond to the overall business cycles (which is measured through $y$ ) rather than its components.

We use the tax equation to model automatic stabilizers, i.e., the endogenous response of tax revenue to GDP fluctuations (without deliberate changes in policy). The equation thus takes the form:

(3) \begin{equation} \tau _t = \alpha _{\tau ,y} y_t + \alpha _{\tau ,g} g_t + \alpha _{\tau ,is} is_t+\alpha _{\tau ,ip} ip_t+\varepsilon _{\tau t}, \end{equation}

where we expect the automatic stabilizer $\alpha _{\tau ,y}$ to be positive as (tax) revenue increases in income. While most of our informative priors regarding elasticities are quantitatively small, there has been some evidence that this automatic stabilizer is relatively large. For the case of the US, Blanchard and Perotti (Reference Blanchard and Perotti2002) estimate the size of the automatic stabilizer to be 1.85, while Caldara and Kamps (Reference Caldara and Kamps2017) show that the implied value for the automatic stabilizer is 3.2 with the Mountford and Uhlig (Reference Mountford and Uhlig2009) method. On the other end of the scale, Perotti (Reference Perotti2004) summarizes the estimated value of $\alpha _{\tau ,y}$ for West Germany, the UK, and Austria to be less than 1. Since progressive taxes (i.e., mostly income tax) that contribute to high automatic stabilizer play a relatively small role in China compared to profit and value-added taxes (VAT), we set the location parameter of the prior for $\alpha _{\tau ,y}$ to $1$ with a scale parameter of 0.2, implying a 92% prior probability that $\alpha _{\tau ,y}$ falls in the range from $0.5$ to $1.5$ .

We assume that revenue increases in income in general and by and large independent of the individual contributions of different demand components. To get a clearer identification, we therefore restrict both investment coefficients in this equation to $0$ . As for the government expenditure elasticity on tax $\alpha _{t,g}$ , Blanchard and Perotti (Reference Blanchard and Perotti2002) argue that decisions on tax policy are usually made after that for government expenditure, so $\alpha _{t,g}\neq 0$ . Even though this might not be the case for China, we do not impose 0 restriction on $\alpha _{t,g}$ . Instead, we specify a prior with a location parameter of 0 for this elasticity.

Note that neither equation includes $m_{t}$ , reflecting that we believe the correlation of monetary policy and fiscal policy to be driven by the government rather than the central bank. i.e., we treat monetary policy as being affected by the fiscal policy rather than the other way around. The money equation itself does not include any zero restrictions. Note that money generation is a combination of monetary policy and endogenous money creation. We thus adopt a prior with a modestly positive location parameter for the investment elasticities( $\alpha _{m,is}$ and $\alpha _{m,ip}$ ), as the investment is largely credit financed, which implies money creation. The location parameter for the prior of the income elasticity ( $\alpha _{m,y}$ ) is $0$ . While not negative, this still implies that monetary policy counteracts fluctuations in the business cycle, as the increase in money demand due to increasing income is not accommodated by a corresponding increase in liquidity. Our identification strategy interprets China’s policy coordination as fiscal-led. This is achieved by allowing monetary policy to respond contemporaneously to fiscal variables (government spending, g, and taxes, $\tau$ ), while excluding monetary factors from the structural equations of g and $\tau$ . Consequently, any monetary support for fiscal actions—captured by the inclusion of fiscal variables in the monetary policy reaction function—is considered an integral part of the fiscal policy package. A monetary policy shock is thus strictly defined as the component of monetary policy that is uncorrelated with both fiscal policies and common policy objectives.

Regarding investment, we aim to avoid binding restrictions, since we do not want to force the variables we are most interested in. The one restriction we do impose is that we assume that SOE investment does not respond to private investment but vice versa. While private investment decisions might take SOE investment as a signal and respond quickly, it seems unlikely that SOEs respond to private investment within a quarter. Not only does SOE planning require more time, but their objective function is also quite different, and thus their decisions respond largely to government needs (as reflected by $m$ , $g$ , and $\tau$ ), and demand (as reflected by $y$ ). Since we do not know in advance whether the SOE investment has leading or crowding out effects on non-SOE investment, we will not impose any sign restrictions (or informative priors on the sign) of $\alpha _{ip,is}$ .

The priors for the response of both investment variables to income and money are positive (i.e., we impose $\alpha _{is,m}\gt 0$ , $\alpha _{ip,m}\gt 0$ , $\alpha _{is,y}\gt 0$ , and $\alpha _{ip,y}\gt 0$ ), as we believe both increasing demand and expansionary monetary policy ought to push investment. We assume both to respond negatively to increasing taxes (i.e., we impose $\alpha _{is,\tau }\lt 0$ and $\alpha _{ip,\tau }\lt 0$ ). Regarding the impact of government spending, our prior distribution implies a $93\%$ probability that $\alpha _{is,g}$ is positive as the government can leverage SOEs to increase demand. However, we remain agnostic regarding the value of the effect of spending on private investment ( $\alpha _{ip,g}$ ), as both crowding out or the demand effect might dominate in the short run.

For the GDP equation, we have positive priors on the effects of all GDP components (i.e., SOE investment, private investment, and government spending $\alpha _{y,g}\gt 0$ , $\alpha _{y,is}\gt 0$ , and $\alpha _{y,ip}\gt 0$ ). The positive effect of investment is undisputed in the literature. There is some debate on the effects of government spending, but models that look at the actual spending (such as VAR models) rather than policy decisions typically find a positive short-term effect (Ramey, Reference Ramey2011). We use a negative prior but no binding sign restriction on the impact for government revenue $\alpha _{y,\tau }$ . We only use a mildly negative prior (with a location parameter of $-0.1$ and a scale parameter of $0.1$ ), implying a roughly 20% probability of a positive sign, to account for the fact that output typically only responds sluggishly to tax changes.

The matrix $A$ thus takes the form:

\begin{equation*} A= \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} 1 & -\alpha _{y,g} & -\alpha _{y,\tau } & 0 & -\alpha _{y,is} & -\alpha _{y,ip}\\ -\alpha _{g,y} & 1 &-1& 0& -\alpha _{g,is} & -\alpha _{g,ip} \\ -\alpha _{\tau ,y} & -\alpha _{\tau ,g}& 1 &0 & 0 & 0\\ -\alpha _{m,y} & -\alpha _{m,g} & -\alpha _{m,\tau } & 1 &-\alpha _{m,is} &-\alpha _{m,ip}\\ -\alpha _{is,y} & -\alpha _{is,g} & -\alpha _{is,\tau } & -\alpha _{is,m} &1 & 0\\ -\alpha _{ip,y} & -\alpha _{ip,g} & -\alpha _{ip,\tau } & -\alpha _{ip,m} &-\alpha _{ip,is} & 1 \end{array}\right] \end{equation*}

It is important to distinguish our identifying assumptions from traditional sign or zero restrictions. The latter are typically applied to the IRFs ( $A^{-1}$ ), while most of our restrictions are placed on the structural matrix A itself. A key illustration is the parameter $a_{\tau ,m}=0$ , which imposes a zero restriction on the direct contemporaneous effect of money on tax revenue through the structural equation for $\tau$ . However, our model’s structure implies a positive overall prior through indirect channels: monetary policy affects investment, which drives GDP (y), and thereby increases tax revenue. The existence and sign of these indirect contemporaneous links are grounded in established theoretical and empirical work.

Nevertheless, to achieve precise identification of fiscal shocks, we do impose a minimal set of restrictions directly on the impulse responses. Under a stimulus shock, which results in an increase in the deficit, government expenditure increases while the tax decreases. Government expenditure and tax both increase on the impact of a government size shock. Instead of imposing strict sign restrictions on IRFs, we set priors for the IRFs, with the majority of the cumulative density in the range of the intended sign. For example, we set the priors of the contemporaneous effect of tax revenue to a stimulus shock ( $A^{-1}(3,2)$ ) as Student’s t-distribution with a location parameter of $-0.2$ and a scale parameter of $0.1$ , which means that this impulse response of taxes has a prior of 93% probability to be negative. We still allow a positive impulse response of tax on the impact of a stimulus shock, but with a rather small probability. This practice resembles the merits of BH methods, which not only incorporate the uncertainty caused by the limited sample size but also those caused by our limited knowledge about the correct restrictions. Finally, we impose a positive sign on the determinant of $A$ with a probability of 95%, following Baumeister and Hamilton (Reference Baumeister and Hamilton2019).Footnote ⁵

Table 1 summarizes the details for all prior distributions of all elasticities and the elements of the $A^{-1}$ where we impose informative priors. In the case of China, there is barely any evidence of those elasticities in the literature. We therefore use relatively conservative numbers and put the largest cumulative density of the prior distributions between -1 and 1 for most elasticities except for the automatic stabilizer $\alpha _{\tau ,y}$ .Footnote ⁶

Table 1.

Prior distribution

Our identification strategy, consistent with Bayesian sign-restriction approaches, yields set identification. Although incorporating more restrictive priors would narrow the confidence sets, we intentionally adopt an agnostic framework to prevent the identifying assumptions from dictating the results. The ensuing analysis demonstrates that this limited set of assumptions is sufficient to generate economically meaningful and plausible impulse responses. A key finding is that the long-run effects of a government size shock on revenue and spending are statistically indistinguishable, even though no long-run restrictions were imposed. This result increases our confidence that the model correctly identifies government size shocks separately from short-term stimulus shocks.

2.2 Microdata-based local projections

In the second part of the paper, we use the annualized shocks identified from our SVARFootnote ⁷ in a local projections framework to assess their impact on different firms using an unbalanced firm-level panel from 1998 to 2007 covering $80,000$ to $260,000$ observations per year, yielding a total of slightly less than 1.4 million observations after we clean the data.Footnote ⁸ As we are interested in the different impacts of policy shocks on different types of firms, our key parameter of interest is the interaction of the ownership structure and fiscal policy shocks.

Different arguments have been made regarding the most appropriate definition of an SOE; see Section 3.2 for more details. The emerging consensus seems to be to look at the actual ownership structure rather than using official designations. We follow this argument for our baseline specification and define SOEs based on the state share of the firm’s capital. Rather than selecting a specific threshold for government ownership that defines whether a company is considered state-owned, we borrow from the literature on structural break testing and estimate our model for a range of thresholds. Since many SOEs are fairly large, we control for the interaction of firm size in terms of log total assets ( $size$ ) and the fiscal policy shock variable. Instead of using a battery of firm-specific controls, we manage unobserved heterogeneity using fixed effects (in addition to firm size and state share to avoid biased estimation of the interaction term). This approach yields the following model:

(4) \begin{equation} \begin{split} inv_{i,t+h} = & \beta ^{(h)}_{1} {\unicode{x1D7D9}}_{s_{i,t}\geq \tau } \times shock_t + \beta ^{(h)}_{2} size_{i,t} \times shock_t\\ & + \beta ^{(h)}_{3} size_{i,t} + \beta ^{(h)}_{4} s_{i,t} + u^{(h)}_i + v^{(h)}_t + \varepsilon ^{(h)}_{i,t}, \end{split} \end{equation}

where $inv$ is the log difference of real fixed assets; $s$ is the state share; $t$ and $i$ are time and firm indices, respectively; $u$ , $v$ , and $\varepsilon$ are the components of the compound error term; and $h$ is the forecast horizon. The shock indicator can be either the stimulus shock or the government size shock identified from the SVAR. Since the firm-level data are annual, whereas the shock data are quarterly, we use the sum of shocks over the year to compute an annual shock.

$\tau$ is the threshold that determines the definition of an SOE. We use conditions ranging from $s\gt 0$ over $s\geq 0.1$ , $s\geq 0.2$ , etc., to $s=1$ . The model is run for forecast horizons 0 (i.e., on impact) to 2 (i.e., two years ahead).

Additionally, rather than dividing our sample into SOE versus non-SOE samples, we use a continuous measure, namely, the share of government ownership itself, yielding the following:

(5) \begin{equation} \begin{split} inv_{i,t+h} = &\beta ^{(h)}_{1} s_{i,t} \times shock_t + \beta ^{(h)}_{2} size_{i,t} \times shock_t + \beta ^{(h)}_{3} size_{i,t} \\ & + \beta ^{(h)}_{4} s_{i,t} + u^{(h)}_i + v^{(h)}_t + \varepsilon ^{(h)}_{i,t} \end{split} \end{equation}

Finally, as a robustness check, we include the official SOE designations (described in more detail in the Data section) instead of the threshold-based dummy in Equation 4.

3.1 Macrodata

Except for the series for government revenue, all of our time series are taken from the Federal Reserve Bank of Atlanta’s China’s Macroeconomy: Time Series Data (CMTS data) based on Chang et al. (Reference Chang, Chen, Waggoner and Zha2015). Government spending is computed as the sum of government consumption and government investment (gross fixed capital formation) following Mountford and Uhlig (Reference Mountford and Uhlig2009). We exclude transfer payments, which would move procyclically. Government revenue (or more precisely, tax revenue) is taken from the CEIC database.

The CMTS data contain disaggregated fixed capital formation data, allowing us to observe the heterogeneous effects of policies on the investment of SOEs and non-SOEs. The original data distinguish five categories of investment: government, household, SOE, private, and other non-SOE investments. For our non-SOE sector, we include both private (enterprises) and (other) non-SOE data following the terminology of Chang et al. (Reference Chang, Chen, Waggoner and Zha2015). SOE investment is taken from the dataset as given; i.e., we do not consider government investment to be part of SOE investment.Footnote ⁹

All of the data are at a quarterly frequency. The CMTS data come with seasonal adjustments. Chinese tax revenue data are reported in a way that reflects the actual economic activity in the corresponding quarter rather than merely being driven by the fiscal year. We seasonally adjust the government revenue data by means of X13.

The GDP, investment, and fiscal policy series are in real per capita form adjusted by their corresponding price indices (the GDP deflator and price index for fixed capital formation) and the total population of China. We use the log difference for all data series.

Our data are limited by the availability of SOE investment data, which are currently reported only for the quarters until the end of 2017. We begin our sample after the major reforms of the tax system in the mid-1990s, most notably the reform of 1994, which aimed at increasing the central government’s control over tax revenue, and the 1995 amendment to the tax collection law, which mainly regulated the issuance of Fapiao, certificates for the tax payments. We therefore start our sample from 1996, yielding a sample period of 1996Q1 to 2017Q4.

3.2 Firm-level data

The firm-level data are from the Chinese industrial enterprise database provided by the National Bureau of Statistics of China. The dataset includes balance sheet data for all SOEs and private enterprises above the nationally designated scale for 1998 to 2007.Footnote ¹⁰ Since investment is not reported in the database, we compute it based on fixed assets and depreciation and normalize it by lagged fixed assets, yielding $(k_t-k_{t-1}+d_t)/k_{t-1}$ , where $k$ denotes fixed assets and $d$ is current depreciation. As we cannot compute the growth rate for the first year of our observations, our local projections are based on a sample starting in 1999. The data were collected until 2014. However, data quality deteriorated for the period after 2007, with the number of firms sampled declining and key variables missing for several waves of the survey. For this reason, we focus on the data for the period up to 2007, i.e., the global financial crisis.

Two official designations for SOEs are used in the database. First, there is an indicator for registration as a SOE (henceforth referred to as the SOE registration dummy). Second, there is an indicator for the firm’s ownership, which shows the fractions of capital controlled by central or local governments or government-owned entities, such as other SOEs (henceforth called the state control dummy). However, Hsieh and Song (Reference Hsieh and Song2015) have found that almost half of state-owned firms in this database take the legal form of—and are correspondingly registered as—private enterprises in 2007. Thus, as mentioned in the Model section, our baseline results focus on the state share, i.e., the ratio of state capital over total capital.

After removing outliers, firms with missing industry data, and implausible characteristics (such as a negative state share or a state share above $100\%$ ), we are left with more than 1.3 million observations.

Table 2 summarizes the share of SOEs in the firm-level data using different definitions of state ownership. For the full sample, about $16\%$ of firms are partially owned by the government, and $11\%$ are fully owned by the government. However, since SOE firms are relatively large, those shares represent $30\%$ and $17\%$ , respectively, of total assets. Interestingly, for the 5% of observations under mixed ownership (i.e., that belong to the 16% with at least partial state ownership but not the 11% with full state ownership), the state share is characterized by a relatively uniform distribution, encompassing everything from small investments to majority participation and near-complete government ownership.

Table 2.

Shares of SOEs

Note: SOE1: state capital $\gt 0$ ; SOE2: state capital $\geq 0.5$ ; SOE3: state capital $=1$ .

The Chinese government has identified certain industries—labeled as strategic and pillar industries—as key areas of interest. Strategic industries are relevant for national security or future industrial development, such as gas, oil, and electricity-related industries.Footnote ¹¹ Pillar industries contribute strongly to Chinese GDP and are deemed essential for economic prosperity, such as the manufacturing of chemicals, machinery, and equipment, as well as metal mining and processing.

SOEs are the dominant force in strategic industries, with fully state-owned firms constituting 50% by number but only 40% by total assets. This counterintuitively indicates that the largest strategic firms are primarily private. The prevalence of natural monopolies in this category may explain why smaller, government-run firms persist. Interestingly, the share of SOEs in pillar industries aligns with the full-sample average, implying that direct ownership is not the government’s primary tool for influencing this sector.

Figure 1.

SVAR identified shocks.

5.1 Consumption

The inclusion of consumption expands the VAR system by adding a new equation for consumption and introducing a term for the contemporaneous consumption into each of the original six equations. Our identification assumes that consumption does not affect government expenditure, tax revenue, M2, or investment directly within the period; any contemporaneous effect on these variables is transmitted indirectly through the impact of consumption on GDP, which responds to consumption through the national accounting identity. Since our data are in log difference, the parameter $\alpha _{y,c}$ represents the elasticity of output with respect to consumption. Given that China’s consumption share has been extraordinarily low—averaging around 40% during our sample period—a value well below 1 is theoretically grounded. Consequently, we impose a prior on $\alpha _{y,c}$ as a positively truncated Student’s t—distribution with a location parameter of 0.5 and a scale parameter of 0.2. This prior places a 95% probability on an elasticity below 1, consistent with the observed consumption share.

For the consumption equation:

(6) \begin{equation} c_{t}=\alpha _{c,y}y_{t}+\alpha _{c,g}g_{t}+\alpha _{c,\tau }\tau _{t}+\alpha _{c,m}m_{t}+\alpha _{c,Is}Is_{t}+\alpha _{c,Ip}Ip_{t}+\varepsilon _{ct} \end{equation}

Mirroring our earlier identification strategy, we assume that investment and monetary shocks do not affect consumption directly within the period, but only indirectly through their impact on GDP. This is formalized by setting the parameters $\alpha _{c,Is} = \alpha _{c,Ip} = \alpha _{c,m} = 0$ . For the response of consumption to income, standard theory with a constant marginal propensity to consume suggests a unitary elasticity ( $\alpha _{c,y} = 1$ ). However, empirical evidence consistently shows that consumption responds positively, though less than proportionally, to income shocks in the short run. We therefore center the prior for $\alpha _{c,y}$ at 0.5. Finally, while direct income taxes are low in China, the high share of VAT in total revenue means the tax system still significantly discourages consumption. To reflect this, we set the prior for $\alpha _{c,\tau }$ with a location parameter of −0.5.

The effect of government spending on consumption remains a contested issue in the literature. Theoretically, predictions are divided: Real Business Cycle models typically forecast a decline in consumption due to a negative wealth effect, whereas New Keynesian models often predict an increase. Empirical studies employing SVAR analyses generally report positive effects (see, e.g., Fatas and Mihov, Reference Fatas and Mihov2001; Blanchard and Perotti, Reference Blanchard and Perotti2002; Caldara and Kamps, Reference Caldara and Kamps2008; Ravn et al., Reference Ravn, Schmitt-Grohé and Uribe2012), while those using narrative approaches, such as the Ramey-Shapiro dummy method, often find negative effects (Perotti, Reference Perotti2008). It is crucial to note that these documented effects are derived from IRFs and do not represent a structural elasticity. Given the absence of a clear consensus, we impose no sign restriction on the contemporaneous elasticity parameter $\alpha _{c,g}$ . We instead adopt an agnostic prior, specifying a symmetric Student’s t-distribution with a location parameter of 0 and a scale parameter of 0.2. This places a 98.5% probability on the elasticity falling within the range [−1, 1]. Complete prior specifications are detailed in Table 4.

Table 4.

7-variable SVAR with consumption: Prior distribution

Figure 6.

7-variable SVAR with consumption: Investment difference between SOEs and non-SOEs.

Figures 6 and 7 present the IRFs. The statistical significance at the macro level is reduced. It seems that the cost of increased model complexity and fewer degrees of freedom outweighs the informational benefit of including more variables. This pattern holds across all three robustness checks. However, the median investment difference is still negative for government size shocks and positive for stimulus shocks. The microlevel results remain significant and consistent with the macro direction. These findings match our earlier results from the six-variable model. Two notable differences emerge in the microlevel responses to the stimulus shock. First, the investment difference remains persistently positive without any sign of reversal. Second, SOE investment in the strategic sector falls below that of non-SOEs, marking a stark contrast with the baseline results. It is noteworthy that in this specification, the stimulus shock is driven more by government spending than by tax reductions (Appendix Figure 13). This implies that government support for strategic SOEs appears to rely more on tax relief mechanisms than on direct spending, whereas SOEs in other sectors benefit more from expenditure-based stimulus. The leading role of SOEs, indicated by a sign reversal in the investment difference, is most evident in tax-cut-led stimulus. This pattern is robust across all 7-variable VAR specifications.

Figure 7.

7-variable SVAR with consumption: Microlevel evidence.

5.2 Inflation

For an additional robustness test, we augment the model by including an inflation equation, specified as:

(7) \begin{equation} \pi _{t}=\alpha _{\pi ,y}y_{t}+\alpha _{\pi ,g}g_{t}+\alpha _{\pi ,\tau }\tau _{t}+\alpha _{\pi ,m}m_{t}+\alpha _{\pi ,Is}Is_{t}+\alpha _{\pi ,Ip}Ip_{t}+\varepsilon _{\pi t} \end{equation}

and correspondingly add $\pi$ to the original six equations.

Although our analysis does not focus on price movements per se, we include inflation for two key methodological reasons. First, given the central role of prices in the macroeconomic transmission of shocks, their inclusion can reduce uncertainty in the reduced-form VAR, thereby sharpening the estimates of our structural model. Second, and more critically, modeling inflation is essential for the identification of monetary policy shocks, which in turn helps to isolate fiscal policy shocks more clearly.

We specify the money equation as a policy reaction function, reflecting the importance of money supply in the PBoC’s framework. Consequently, we restrict the parameter for the policy response to inflation $\alpha _{m,\pi }$ to be negative. Conversely, we impose a positive restriction on $\alpha _{\pi ,m}$ , reflecting the standard assumption that an expansion in the money supply exerts upward pressure on prices.

Beyond its role in the monetary policy reaction function, we remain largely agnostic regarding the interactions between prices and other variables. Specifically, we impose no sign restrictions on $\alpha _{\pi ,y}$ or $\alpha _{y,\pi }$ thereby avoiding a forced interpretation of the output and inflation equations in terms of demand or supply shocks. Similarly, we do not restrict the response of inflation to government spending. The literature offers no clear consensus on this relationship: while some studies find expansionary fiscal policy to be inflationary (Caldara and Kamps, Reference Caldara and Kamps2008; Ferrara et al., Reference Ferrara, Metelli, Natoli and Siena2021), others find deflationary effects (Mountford and Uhlig, Reference Mountford and Uhlig2009). Perotti (Reference Perotti2004) reports small effects of government spending on inflation. Furthermore, Jørgensen and Ravn (Reference Jørgensen and Ravn2022) note a discrepancy where standard New Keynesian models predict a positive effect that is not consistently borne out empirically. Given this lack of a consistent theoretical or empirical consensus, we specify a symmetric prior centered around zero for $\alpha _{\pi ,g}$ . The details of these prior settings are provided in Table 5.

Table 5.

7-variable SVAR with inflation: Prior distribution

Figure 8.

7-variable SVAR with inflation: Investment difference between SOEs and non-SOEs.

The IRF results in Figure 8 show that the significance level of macro-level investment difference responses is reduced, but the direction of response matches the findings in the 6-variable system. Moreover, the macro and micro results (Figures 8 and 9) remain qualitatively aligned, and the core conclusions of our baseline model are unchanged.

Figure 9.

7-variable SVAR with inflation: Microlevel evidence.

5.3 International trade

We conduct a final robustness test by augmenting our model to include the trade balance. While international trade is a fundamental component of China’s economic growth, its effects—such as resource reallocation, technology spillovers, and efficiency improvements—typically manifest over time rather than instantaneously. We therefore impose zero restrictions on most contemporaneous relationships.

The equation for the international trade is:

(8) \begin{equation} NX_{t}=\alpha _{nx,y}y_{t}+\alpha _{nx,g}g_{t}+\alpha _{nx,\tau }\tau _{t}+\alpha _{nx,m}m_{t}+\alpha _{nx,Is}Is_{t}+\alpha _{nx,Ip}Ip_{t}+\varepsilon _{nxt} \end{equation}

We proxy net exports using the log ratio of exports to imports.Footnote ²⁰ In our identification, trade is restricted to affect only output contemporaneously, and we impose a positive prior on the elasticity $\alpha _{y,nx}$ with a location parameter of 0.1 and a scale parameter of 0.2. All other variables are assumed to be unaffected by trade within the period.

This zero restriction on the monetary response ( $\alpha _{m,nx}=0$ ) is justified by two factors. First, although strict capital controls and mandatory currency conversion for trade companies would, in theory, increase the money supply, the People’s Bank of China actively sterilizes such exogenous inflows to maintain its monetary policy targets. Second, the timing of goods flows and corresponding payments often does not coincide, further weakening the case for a contemporaneous link.

Our identification strategy assumes that investment does not affect net exports contemporaneously. We do, however, allow for a direct effect of output ( $y$ ) on net exports, while remaining agnostic about its sign. The impact of fiscal and monetary policy on the trade balance is theoretically ambiguous, as it depends on the specific policy implementation and its transmission through channels such as capital flows, interest rates, and exchange rates. Nevertheless, empirical studies, including those by Lane and Perotti (Reference Lane and Perotti1998), Monacelli and Perotti (Reference Monacelli and Perotti2010), Miyamoto et al. (Reference Miyamoto, Nguyen and Sheremirov2019), and Ferrara et al. (Reference Ferrara, Metelli, Natoli and Siena2021), consistently find that increased government spending deteriorates the trade balance. In line with this evidence, we center the prior for $\alpha _{nx,g}$ around a negative value but do not impose a binding sign restriction. For the remaining policy variables, the priors are centered around zero. Complete details of all prior specifications for trade-related parameters are provided in Table 6.

Table 6.

7-variable SVAR with NX: Prior distribution

As shown in Figures 10 and 11, the IRF results under this specification exhibit minor quantitative differences but are qualitatively consistent with those from our baseline model, demonstrating the robustness of our findings.

Figure 10.

7-variable SVAR with NX: Investment difference between SOEs and non-SOEs.

Figure 11.

7-variable SVAR with NX: Microlevel evidence.