Estimating the impact of the financial cycle on fiscal policy

Abstract

We investigate the impact of the financial cycle on fiscal policy by estimating fiscal multipliers for different types of government spending that are contingent on two states determined by the financial cycle. To obtain our estimates, we extend the threshold VAR method from a single country to a panel of high-income countries. Our results indicate that the multiplier for government investment is affected by the state of the financial cycle: while the initial impact is positive for both states, in an upturn it turns negative, while in a downturn it remains positive. In the case of government consumption, the multiplier does not seem to significantly depend on the financial cycle. However, jointly conditioning on the financial and business cycles produces multipliers of government consumption which vary over the states of both cycles. This contrasts with the results for government investment which are left essentially unchanged by the joint conditioning on the four states defined by both cycles.

Appendices

A State space model of CPB financial cycle

We denote the credit data for country i by $y^1_{it}$ and the housing price index by $y^2_{it}$ and define the data column vector $\vec {y}_{it}=\left( y^1_{it}, y^2_{it}\right) '$. Similarly, we denote the vector of the financial cycles for credit and the housing price index of country i as $\vec {f}_{it}$. We use the same notion for the vector of the business cycle components, $\vec {b}_{it}$. The state space model also includes two local linear trend components, one for credit and one for the housing price index, giving rise to the vector $\vec {\mu }_{it}$ to capture the growth dynamics in the data. Each trend component is itself affected by a random walk growth component, which for both series we also denote by a vector: $\vec {\beta }_{it}$. Using this notation we can express the model in Luginbuhl et al. (2019) as follows³⁵:

$$\begin{aligned} \vec {y}_{it}= & {} \vec {\mu } _{it} + \vec {f} _{it} + \vec {b} _{it} + \vec {\varepsilon } _{it}, \quad \vec \varepsilon _{it} \sim N\left( 0,\Omega _{\varepsilon ,it} \right) , \\ \vec {\mu } _{it}= & {} \vec {\mu } _{i,t - 1} + \vec {\beta } _{i,t - 1} + \vec {\eta } _{it}, \quad \vec \eta _{it} \sim N\left( 0, \Omega _{\eta ,i} \right) , \\ \vec {\beta } _{it}= & {} \vec {\beta } _{i.t - 1} + \vec {\zeta } _{it}, \quad \vec \zeta _{it} \sim N\left( 0, \Omega _{\zeta ,i} \right) , \end{aligned}$$

where the financial cycle component is given by

$$\begin{aligned} \left( {\begin{array}{*{20}{c}} {{\vec {f} _{it}}}\\ {\vec {f} _{it}^{*}} \end{array}} \right) = {\rho _i ^f}\left( {\begin{array}{*{20}{c}} {\cos {\frac{2 \pi }{\lambda _i ^f}}}&{}\quad {\sin {\frac{2 \pi }{\lambda _i ^f}}}\\ { - \sin {\frac{2 \pi }{\lambda _i ^f}}}&{}\quad {\cos {\frac{2 \pi }{\lambda _i ^f}}} \end{array}} \right) \otimes I_2 \left( {\begin{array}{*{20}{c}} {{\vec {f} _{i,t - 1}}}\\ {\vec {f} _{i,t - 1}^{*}} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {{\vec {\kappa } _{it}^f}}\\ {\vec {\kappa } _{it}^{f*}} \end{array}} \right) , \end{aligned}$$

and the business cycle component by

$$\begin{aligned} \left( {\begin{array}{*{20}{c}} {{\vec {b} _{it}}}\\ {\vec {b} _{it}^{*}} \end{array}} \right) = {\rho _i ^b}\left( {\begin{array}{*{20}{c}} {\cos {\frac{2 \pi }{\lambda _i ^b}}}&{}\quad {\sin {\frac{2 \pi }{\lambda _i ^b}}}\\ { - \sin {\frac{2 \pi }{\lambda _i ^b}}}&{}\quad {\cos {\frac{2 \pi }{\lambda _i ^b}}} \end{array}} \right) \otimes I_2 \left( {\begin{array}{*{20}{c}} {{\vec {b} _{i,t - 1}}}\\ {\vec {b} _{i,t - 1}^{*}} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {{\vec {\kappa } _{it}^b}}\\ {\vec {\kappa } _{it}^{b*}} \end{array}} \right) . \end{aligned}$$

Note that the components $\vec {b}_{it}^{*}$ and $\vec {f}_{it}^{*}$ are only required for the construction of the cycle components $\vec {b}_{it}$ and $\vec {f}_{it}$. Also note that the model contains the vector disturbance terms $\vec \varepsilon _{it}$, $\vec \eta _{it}$, $\vec \zeta _{it}$, as well as $\vec \kappa _{it}^C \sim N\left( 0, \Omega _{\kappa ,i}^C \right)$ and $\vec \kappa _{it}^{C*} \sim N\left( 0, \Omega _{\kappa ,i}^C \right)$ for $C=b$ or f.³⁶

The state space model (Luginbuhl et al. 2019) use in the estimation of the financial cycle is closely related to work of Rünstler and Vlekke (2018) and Winter et al. (2017), which are also based on unobserved cycle components to model financial cycles. The main difference here being that the estimation method by Luginbuhl et al. (2019) imposes the restriction of there being only one shared stochastic process driving both financial cycle components in their bi-variate model. This restriction is necessary to help identify one financial cycle for each country. In fact the financial cycle estimate $f_{it}$ is the cycle component for the credit data. Although the housing price index shares the same stochastic disturbance driving the cycle, the housing price index has its own starting value. As a result, the housing price index financial cycle can deviate from the credit cycle in the initial part of the sample period.³⁷

The bi-variate state space models distinguish between the business cycle and the financial cycle by assuming that the financial cycle has a longer period cycle than the business cycle. The financial cycles are full-information, Kalman smoothing estimates obtained using Bayesian Markov Chain Monte Carlo or MCMC methods.

B Data series

See Tables 4 and 5.

Table 4 Data for benchmark specification

Table 5 Government investment, Oxford Economics series linked to data described below

C Correlation and phase concordance between financial and business cycles

See Tables 6 and 7.

Table 6 Correlation and phase concordance between the financial, BIS and business cycle

Table 7 Overlap between financial cycle and business cycle phases

D IRFs of inflation and real interest rate, baseline specification

See Figs. 5 and 6.

Fig. 5

Impulse responses: inflation. See Sect. 5 for an elaboration on these results, and the note to Fig. 2 for a description of the construction of the confidence bands

Fig. 6

Impulse responses: real interest rate. See Sect. 5 for an elaboration on these results, and the note to Fig. 2 for a description of the construction of the confidence bands

E Baseline results in alternative specifications

1.1 E.1 Figures for baseline results in alternative specifications

See Figs. 7, 8 and 9.

Fig. 7

Cumulative fiscal multipliers with an endogenous threshold. See the note in Fig. 2 for more information

Fig. 8

Detrending with the projection method. We detrend all non-stationary variables using the projection method, where we follow Hamilton (2018) and project the variable at time $t+8$ onto the four most recent values $t-3,\ldots ,t$. See the note in Fig. 2 for more information

Fig. 9

Cumulative fiscal multipliers using weighted mean group estimation. We only use 2 lags instead of 4 because of a shortage of degrees of freedom at the country level. We weight the country-specific cumulative fiscal multipliers using number of observations per country as weight and take the average to construct the weighted mean group estimate. See the note in Fig. 2 for more information

1.2 E.2 Alternative financial cycles

See Figs. 10, 11 and 12.

Fig. 10

Cumulative fiscal multipliers using the BIS cycle as financial cycle. See the note in Fig. 2 for more information

Fig. 11

Cumulative fiscal multipliers using credit-to-GDP gap as financial cycle. See the note in Fig. 2 for more information

Fig. 12

Cumulative fiscal multipliers using the Schüler financial cycles. See the note in Fig. 2 for more information

F Additional figures of the robustness checks

See Figs. 13, 14, 15, 16 and 17.

Fig. 13

Cumulative fiscal multipliers with yearly data. The model is estimated with year data and include $L=1$ lags. See the note in Fig. 2 for more information

Fig. 14

Cumulative fiscal multipliers with private GDP as first endogenous variable. Private GDP is ordered as the first endogenous variable. Therefore, the cumulative multipliers are equal to one by construction in the first period. See the note in Fig. 2 for more information

Fig. 15

Cumulative fiscal multipliers including debt-to-GDP as endogenous variable. Government debt-to-GDP is added to the baseline model as additional endogenous variable and is ordered between government spending real GDP. (Color figure online)

Fig. 16

Cumulative fiscal multipliers with three regimes and two endogenous thresholds. See the note in Fig. 2 for more information

Fig. 17

Cumulative fiscal multipliers for total government expenditure. See the note in Fig. 2 for more information