I am especially indebted to Stephanie Schmitt-Grohé and Barbara Rossi for their guidance, support and encouragement. I would also like to thank the editor, Jesus Fernandez-Villaverde and two anonymous referees for their insightful comments, and Francesco Bianchi, Craig Burnside, Vasco Curdia, Marco Del Negro, Gauti Eggertsson, Cosmin Ilut, Kent Kimbrough, Juan Rubio-Ramirez, and Andrea Tambalotti for helpful discussions. Part of this article was completed while I was visiting the Federal Reserve Bank of New York, and their hospitality is gratefully acknowledged. The views expressed in this article are those of the author. No responsibility should be attributed to the Bank of Canada.

Original Article

# ON FISCAL MULTIPLIERS: ESTIMATES FROM A MEDIUM SCALE DSGE MODEL

Article first published online: 22 JAN 2014

DOI: 10.1111/iere.12045

© (2014) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association

Additional Information

#### How to Cite

ZUBAIRY, S. (2014), ON FISCAL MULTIPLIERS: ESTIMATES FROM A MEDIUM SCALE DSGE MODEL. International Economic Review, 55: 169–195. doi: 10.1111/iere.12045

#### Publication History

- Issue published online: 22 JAN 2014
- Article first published online: 22 JAN 2014
- Manuscript Revised: JAN 2013
- Manuscript Received: JUL 2011

- Abstract
- Article
- References
- Cited By

### Abstract

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

This article contributes to the debate on fiscal multipliers, in the context of an estimated dynamic stochastic general equilibrium model, featuring a rich fiscal policy block and a transmission mechanism for government spending shocks. I find the multiplier for government spending to be 1.07, which is largest on impact. The multipliers for labor and capital tax on impact are 0.13 and 0.34, respectively. The effects of tax cuts take time to build and exceed stimulative effects of spending by 12–20 quarters. I carry out counterfactual exercises to show how alternative financing methods and expected monetary policy have consequences for the size of fiscal multipliers.

### 1. INTRODUCTION

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

During the recession of 2007–09, countries around the world have taken extraordinary fiscal measures to stimulate their economies with the hope of boosting demand and limiting job losses. For instance, in February 2009, the United States passed a $787 billion American Recovery and Reinvestment Act, which amounts to over 5% of annual GDP. These policy actions, however, have given rise to a heated debate since there is a lack of consensus among economists on the relative stabilizing effects of fiscal policy measures in the form of current tax cuts or increases in spending. The objective of this article is to shed light on this debate in the context of a microfounded medium-scale dynamic stochastic general equilibrium (DSGE) model developed and estimated to explain the effects of discretionary fiscal policy.

The model considered in this article features a rich fiscal block with distortionary labor and capital income taxes and a careful modeling of the government financing behavior. Unlike monetary policy, since there is no widely accepted specification for fiscal policy, this article considers various fiscal rules, allowing fiscal variables to respond to the state of the economy and the level of government debt. Ultimately, the focus is on how the economy responds to fiscal policy actions in the form of changes in government spending, tax rates, and lump-sum transfers.

In addition, the model features a transmission mechanism for government spending shocks, motivated by the fact that most commonly used business cycle models might not be appropriate to study the effects of public spending shocks. As shown in the seminal paper by Baxter and King (1993), when government spending financed by lump-sum taxes rises, households face a negative wealth effect and inevitably lower their consumption. On the other hand, most empirical studies either find a *positive* response of consumption to government spending shocks (e.g., Fatas and Mihov, 2001; Blanchard and Perotti, 2002, who use structural vector autoregressions, VARs), whereas others employing different identification schemes (e.g., Burnside et al., 2004; Mountford and Uhlig, 2009) find an *insignificant* response and private consumption not being crowded out by government consumption.1 The response of private consumption to government spending shocks is important when quantifying the effects on output, since it accounts for over 60% of GDP. Thus, to allow for a channel of transmission of government spending shocks, besides the standard wealth effects, I consider a model that embeds deep habit formation in public and private consumption, as introduced in Ravn et al. (2006). Deep habits imply that agents form habits over individual varieties of goods, as opposed to a composite consumption good. This new feature gives rise to counter-cyclical markups, allowing wages to rise in response to a government spending shock. If this increase is large enough, it induces households to substitute away from leisure to consumption, which can potentially overcome the negative wealth effects.

In this article, I undertake a likelihood-based Bayesian estimation of the structural model. This full-information approach fits the model to all the variation in the data and not just the dynamic effects of a policy shock. Along with standard macroeconomic aggregate variables, I also use fiscal variables as observable. These include data on government spending and time series for labor and capital tax rates, which further allow the model to distinguish between the effects of the two different kinds of tax changes. Using Bayesian techniques I also find the whole posterior distributions of the fiscal multipliers, which are more informative than just point estimates. Finally, an estimated model provides an ideal environment in which to conduct counterfactual exercises.

The article reports the implied multipliers for all the fiscal instruments in the estimated model and shows how the fiscal shocks transmit through the economy. The main results can be summarized as follows: The median multiplier for government spending is found to be 1.07. This means that a 1% of GDP increase in government spending increases GDP overall by 1.07%. The multiplier is larger than 1 since the estimated model predicts a positive response of private consumption to government spending, which is in contrast to models that do not consider a channel of transmission of government spending shocks, but is consistent with other empirical studies. The median multipliers for labor and capital tax on impact are much smaller. A cut in tax revenues of 1% of GDP, driven by labor and capital taxes, causes GDP to increase by 0.13% and 0.34%, respectively. However, in contrast to increased spending which has the maximum impact as soon as the shock hits the economy, the effects of tax shocks take time to build. The stimulative effects of tax cuts exceed the effects of higher spending at horizons of 12–20 quarters and are primarily driven by the response of investment. These results also highlight the fact that multipliers vary significantly across the horizon, and thus the stimulative effect in the short run differs from the effects in the longer run.

This estimated model provides an empirical framework to critically evaluate different fiscal policies. In counterfactual exercises, I examine how alternative financing decisions alter the size of multipliers and the role that automatic stabilizers play in determining the stimulative effect of spending. The results indicate that although the multipliers are mostly unaffected at shorter horizons of up to a year, the method of financing, either by increased deficits or raising taxes more aggressively, is important for longer-run consequences.

I also provide evidence on how expected monetary policy has consequences for the stimulative effects of fiscal measures. The interaction between monetary and fiscal policy has recently gained significant attention, particularly in understanding the consequences of fiscal policy action under current circumstances when nominal interest rates are near zero (see, e.g., Cogan et al., 2010; Eggertsson, 2010; Christiano et al., 2011; Davig and Leeper, 2011). Although I do not explicitly consider the zero lower bound, the results in this article are complementary. I find that the response of the monetary authority to deviations of output from steady state has significant effects on the size of fiscal multipliers. In fact, if the monetary authority is relatively accommodative, then increased spending has a significantly higher stimulative effect. This is however, not the case for all fiscal measures, as shown in the case of labor tax cuts.

Finally, I simulate the impact of the American Recovery and Reinvestment Act of 2009 in the estimated model as a combination of increased government spending and a cut in labor taxes. This fiscal stimulus plan results in a considerable expansion in GDP, with the largest effects predicted in early 2010. These effects on output, however are accompanied by a significant rise in government debt, and since the households are forward-looking and anticipate higher taxes in the future to finance this plan, the stimulative effects on GDP decline rapidly over the course of next few years.

The main distinguishing features of the article are, first, deep habit formation by agents in the economy modeled as a transmission mechanism for public spending shocks, and, second, explicit modeling of fiscal policy with fiscal rules and estimation of the model with data including fiscal variables.

Deep habit formation has not been explored earlier in the context of a medium-scale DSGE model estimated using a full-information approach.2 There is, however, earlier work by Coenen and Straub (2005) and Forni et al. (2009), among others, who explore another transmission mechanism for spending shocks. These papers estimate a model of fiscal policy that extends the work of Gali et al. (2007) and feature a fraction of the population being liquidity constrained to match the empirical evidence on the effects of government spending shocks.3 Note also that in contrast to this article, the focus in the aforementioned papers has primarily been to see if the estimated model can reconcile the positive response of aggregate consumption to government spending. They do not explore detailed fiscal rules or consider the consequences of alternative financing methods and expected monetary policy on fiscal multipliers.4 Other transmission mechanisms explored in the literature include productive government spending (e.g., Leeper et al., 2010), preferences where public and private consumption are complements (e.g., Bouakez and Rebei, 2007) and preferences where negative wealth effects on labor supply are mitigated (e.g., Monacelli and Perotti, 2008). I do not claim that these other mechanisms are empirically irrelevant, but by focusing on deep habit formation, I highlight the role of counter-cyclical markups, endogenously generated by deep habits, for the propagation of fiscal shocks. This countercyclicality of markups is an empirical regularity documented by Bils (1987) and Rotemberg and Woodford (1992), among others.5

In other related work, Leeper et al. (2010) explore the role of using various fiscal instruments for financing debt and consider different fiscal policy rules. However, the effects of government spending shocks are propagated in their model primarily through negative wealth effect and they do not consider a channel that would allow the possibility of consumption rising in response to public spending changes.

The rest of the article is organized as follows: Section 'MODEL' describes the theoretical model. In Section 3, I provide the description of the estimation procedure used. Section 'ESTIMATION RESULTS' presents the estimation results and model dynamics, and Section 'THE ESTIMATED SIZE OF FISCAL MULTIPLIERS' highlights the fiscal multipliers implied by the estimates. Section 'COUNTERFACTUAL FISCAL POLICY EXPERIMENTS' shows some counterfactual exercises to consider alternative financing decisions. In Section 7, I explore the interaction between monetary and fiscal policy. Section 'SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009' shows the simulation of the American Recovery and Reinvestment Act of 2009, and, finally, Section 'CONCLUSION' concludes.

### 2. MODEL

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

This is a medium scale DSGE model based on the work of Christiano et al. (2005). Most features are standard to the literature, such as nominal rigidities in the form of price and wage stickiness and real rigidities in the form of variable capacity utilization and investment adjustment cost. This framework serves as a starting point, since it has been shown to fit the data well, for example, by Del-Negro et al. (2005) and Smets and Wouters (2007). The specific departures include deep habits in public and private consumption, as first introduced in Ravn et al. (2006), as a transmission mechanism for government spending shocks and a detailed fiscal block.

#### 2.1. Households

The economy is populated by a continuum of identical households of measure 1 indexed by . Each household maximizes lifetime utility function, which depends on consumption, , hours worked, and government provided goods, , given by

- (1)

In this formulation, is an intertemporal preference shock, or a shock to consumer's impatience level, and affects both the marginal utility of consumption and marginal disutility of labor. It follows an autoregressive process,6

- (2)

where is the autoregressive coefficient, and is i.i.d. . Households derive utility from consumption of government provided goods, given by here, which is separable from private consumption and leisure. This means that public spending does not affect the marginal utility of private consumption or leisure. The functional form of the utility function is , where γ is the coefficient of relative risk aversion.

The variable is a composite of habit adjusted consumption of a continuum of differentiated goods indexed by ,

- (3)

where denotes the stock of habit in consuming good *i* in period *t*, and the parameter η is the elasticity of substitution between intermediate goods. The parameter measures the degree of external habit formation. The stock of external habit is assumed to depend on a weighted average of consumption in all past periods. Habits are assumed to evolve over time according to the law of motion,

- (4)

The parameter measures the speed of adjustment of the stock of external habit, and when takes the value zero, habit is measured only by consumption in the previous period. This slow decay in habit allows for persistence in markup movements.

For any given level of consumption , purchases of each individual variety of good in period *t* solves the dual problem of minimizing total expenditure, , subject to the aggregation constraint (3), where denotes the nominal price of a good of variety *i* at time *t*. The optimal level of for is then given by

- (5)

where is a nominal price index defined as . Note that consumption of each variety is decreasing in its relative price, and increasing in the level of habit adjusted consumption . The demand function in Equation (5) has a price-elastic component that depends on aggregate consumption demand, and the second term is perfectly price-inelastic. An increase in aggregate demand increases the share of the price-elastic component and thus increases the elasticity of demand, inducing a decline in the markup. In addition to this, firms also take into account that today's price decisions will affect future demand, and so when the present value of future per unit profit is expected to be high, firms have an incentive to invest in the customer base today. Thus, this gives them an additional incentive to appeal to a broader customer base by reducing markups in the current period. This countercyclicality of the price markup has been empirically documented by Bils (1987) and Rotemberg and Woodford (1999), among others.7

Each household *j* is a monopolistic provider of a differentiated labor service and is assumed to supply enough labor, , to satisfy demand,

- (6)

where denotes the real wage charged by household *j* at time *t*, is an index of real wage prevailing in the economy, and is a measure of aggregate labor demand by firms. The parameter is the elasticity of substitution between differentiated labor types. In addition, wage rigidities are modeled as a convex cost of adjusting nominal wages, which is zero at steady state, given by, , where denotes the wage adjustment cost parameter.

The household is assumed to own physical capital, , which accumulates according to the following law of motion:

- (7)

where denotes investment by household *j* and δ is a parameter denoting the rate of depreciation of physical capital.8 Here denotes an efficiency shock to the investment adjustment cost. It also follows an autoregressive process given by

- (8)

where is the autoregressive coefficient, and is i.i.d. .

Owners of physical capital can control the intensity at which this factor is utilized. It is assumed that using the stock of capital with intensity entails a cost of units of the composite final good.9 Households rent the capital stock to firms at the real rental rate per unit of capital. Total income stemming from the rental of capital is given by .

The household *j*'s period-by-period budget constraint is given by

- (9)

where . The variable denotes the real payoff in period *t* of nominal state-contingent assets purchased in period . The variable denotes dividends received from the ownership of firms, and denotes the gross rate of consumer-price inflation. The households face labor and capital income tax rates, given by and , respectively, and get a lump-sum transfer from the government, given by . The term represents a depreciation allowance for tax purposes.10

#### 2.2. Fiscal and Monetary Policy

Households derive utility from public goods that is separable from private consumption and leisure, recalling the expression in (1), and they exhibit good-by-good habit formation for these particular goods also. As motivated in Ravn et al. (2012), the provision of public services in one community, such as street lighting or garbage collection, causes other communities to also want access to those public services.

The government allocates spending over individual varieties of goods, , so as to maximize the quantity of a composite good, , produced with a differentiated varieties of goods according to the following relation:

The parameter measures the degree of habit formation of government consumption, and the variable denotes the government's stock of habit in good *i* and is assumed to evolve as follows:

- (10)

where is the rate of depreciation of the stock of habits. The government's problem consists of choosing , , so as to maximize subject to the budget constraint , where denotes real government expenditures. The resulting demand function for each differentiated good by the public sector is

which is analogous to the demand function for household consumption. Therefore, introducing deep habits in public consumption, along with private consumption, is needed to generate countercyclical markups in response to an increase in both private and public consumption demand.

The fiscal authority issues bonds, and raises tax revenues, and the expenditures include government purchases, and lump-sum transfers to households, . The government budget constraint looks as follows:

- (11)

where tax revenues, are given by

- (12)

Unlike monetary policy, there is no widely accepted specification for fiscal policy. In recent work, Romer and Romer (2010) use narrative evidence to identify the size and reasons behind all major postwar tax policy actions. They find tax policy actions as either being motivated by countercyclical actions or changes in spending, which they call endogenous policy changes, or to deal with an inherited budget deficit or raise long-run growth, classified as exogenous changes in their analysis. They estimate the effects of exogenous tax movements on output and point out that failing to account for influences of economic activity on tax policy leads to biased effects of macroeconomic effects of tax changes. To address such concerns, in this article, taxes are modeled to allow for a systematic response to the state of the economy and a feedback reaction to debt to prevent large debt to GDP ratios, and the processes for tax rates look as follows:11

- (13)

and

- (14)

The response of the tax rates to the level of debt ensures fiscal solvency. For instance, in the case of increased government expenditures, taxes will respond to the increasing deficit so that the intertemporal government budget constraint is satisfied. Note that the tax rates are assumed to respond to lagged values of the debt and output deviations from the steady state. This helps to isolate the effects of fiscal shocks on the economy at least on impact and is a reasonable assumption, as the model is used to match quarterly data.

In addition, since changes in personal income taxes might affect both labor and capital tax rates simultaneously, the innovations to labor and capital income taxes, and , respectively, are modeled to be correlated, similar to Leeper et al. (2010), so that

- (15)

- (16)

Note and are i.i.d. and , respectively. Here the parameter ϕ captures the correlation between the two tax shocks, and would imply that the innovations in labor and capital income tax rates are orthogonal.

Real government expenditures, , have a process with an autoregressive term, a response to lagged output to capture systematic response to output and a feedback reaction to debt,12

- (17)

where is a government spending shock, assumed to be i.i.d. . Lump-sum transfers, , have the following process that also features a response to the state of the economy and level of debt in the economy. The response to the state of the economy captures the fact that, during recessions, transfers automatically go up, for instance, in the form of unemployment and welfare benefits,

- (18)

where represents a shock to transfers and is i.i.d. . Transfers are modeled as neutral payments in the model and primarily play the role of a residual in the government budget constraint. So a transfer shock can be thought of as a shock to the budget constraint not captured by spending or tax shocks.13

The monetary authority follows a Taylor type rule,

- (19)

with interest rate smoothing, governed by the parameter and a response to deviation of inflation and output from their respective steady states, denoted by and , respectively. is a monetary shock and is i.i.d. .

#### 2.3. Firms

Each variety of final goods is produced by a single firm in a monopolistically competitive environment. Each firm produces output using as factor inputs capital services, and labor services, . The production technology is given by

- (20)

where *F* is a homogenous of degree 1, concave function strictly increasing in both its arguments, and ψ introduces fixed costs of operating a firm in each period, and are modeled to ensure a realistic profit-to-output ratio in steady state.14 The variable denotes an exogenous technology shock, following an AR(1) process,

- (21)

where , and is i.i.d. .

The objective of the firm is to choose contingent plans for , , and so as to maximize the present discounted value of dividend payments, given by

where

subject to demand functions for public, private, and investment goods faced by firm *i*. Here denotes aggregate absorption of good *i*, which includes , , and . Note that price rigidities are introduced following Rotemberg (1982) by assuming that the firms face a quadratic price adjustment cost for the good it produces. I choose this specification of price rigidities because the introduction of deep habits makes the pricing problem dynamic and accounting for additional dynamics arising from Calvo-Yun type price stickiness makes aggregation nontrivial.15

#### 2.4. Market Clearing

Integrating over all firms and taking into account that the capital–labor ratio is common across firms, the aggregate demand for the composite labor input, , satisfies and the aggregate effective level of capital, , satisfies this implies a resource constraint that looks as follows:

- (22)

### 3. ESTIMATION

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

The competitive equilibrium conditions of the model are log-linearized around a nonstochastic steady state.16 The system of equations can then be written as follows:

- (23)

where are the model variables, the matrices *F* and *Q* are functions of Λ, and the structural parameters of the model and are the structural shocks in the model.

#### 3.1. Data and Estimation Strategy

Since the focus of this article is fiscal policy in the context of a DSGE model, in a departure from most preexisting Bayesian estimation papers, in addition to aggregate macroeconomic variables, I include fiscal variables as observables. The following quarterly data series, spanning 1958:1–2008:4, are used in the estimation: , where is real per capita consumption, is real per capita investment, is price inflation, is the federal funds rate, is real per capita total government purchases, is real federal debt held by public, is the capital tax rate, and is the labor tax rate.17 Details on the construction of each time series are provided in the online appendix.

The measurement equation connects the observables, to the model variables:

- (24)

The matrix *H* is a function of the structural parameters of the model and denotes measurement errors. The dynamic system is characterized by the state equation (23) and this measurement equation is estimated using Bayesian techniques, where the object of interest is the joint posterior distribution of the parameters, which combines the prior distribution and the likelihood function. The priors for the parameters being estimated are given in the next subsection, and the likelihood is computed using the Kalman filter under the assumption of all the structural shocks being normally distributed. The Metropolis–Hastings algorithm is used to sample from the posterior proposal distribution, which is a multivariate normal, . The algorithm is initialized using the maximized posterior mode from the optimization routine csminwel.m, by Chris Sims, and Σ is the inverse of the numerical Hessian evaluated at this posterior mode. The scaling factor *c* is chosen to ensure an acceptance rate of close to 30%. 1.5 million draws are generated, where the first 500,000 are used as a burn-in period to lose any dependence on initial values. Ultimately, several convergence diagnostics are used to ensure the convergence of these Monte Carlo chains.18

#### 3.2. Calibration and Priors

Some of the parameters that are hard to identify or pin down in steady state are calibrated. These include the discount factor β, set at , which implies a steady-state annualized real interest rate of 3%. The depreciation rate, δ, is set at 0.025, which implies an annual rate of depreciation on capital equal to 10%. The production function parameter θ is set at 0.30, which corresponds to a steady-state share of capital income roughly equal to 30%. The labor elasticity of substitution, is set at 21, and goods elasticity of substitution, η, is set at 5.3, since with the introduction of deep habits the price markup movements are jointly determined by deep habit parameters and η is generally not well identified.

Steady-state variables are also calibrated based on averages over the sample period considered in the article. The share of government spending in aggregate output is set at 0.18, and the annual average of the ratio of debt to GDP pins down the steady-state value to be 0.33. Similarly, the steady-state values of the capital and labor tax rates are based on mean of the constructed series of average tax rates over the sample size and are 0.41 and 0.23, respectively. Steady-state labor is set at 0.5, which corresponds to a Frisch elasticity of labor supply of unity.

Table 1 shows the prior distribution for the parameters being estimated. These are consistent with the literature, and the means of the distribution were set based on estimates from preexisting studies. On the other hand, for fiscal policy rule parameters, the literature is less informative, and so the priors are diffuse and span a larger parameter space. The priors are discussed in detail in the online appendix.19

Prior | Posterior | |||||
---|---|---|---|---|---|---|

Parameter | Description | Dist. | Mean | Std. Dev. | Mean | [5, 95] |

NOTE ^{}B: beta; G: gamma; IG: inverse gamma; and N: normal.
| ||||||

Autocorr. of | B | 0.7 | 0.2 | 0.91 | [0.90, 0.92] | |

Autocorr. of | B | 0.7 | 0.2 | 0.90 | [0.89, 0.92] | |

Autocorr. of | B | 0.8 | 0.2 | 0.92 | [0.88, 0.96] | |

Autocorr. of | B | 0.7 | 0.2 | 0.72 | [0.62, 0.78] | |

Autocorr. of | B | 0.7 | 0.2 | 0.64 | [0.54, 0.73] | |

Autocorr. of | B | 0.7 | 0.2 | 0.79 | [0.76, 0.83] | |

Autocorr. of | B | 0.7 | 0.2 | 0.67 | [0.62, 0.73] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.012 | [0.010, 0.013] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.009 | [0.008, 0.010] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.015 | [0.013, 0.017] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.182 | [0.152, 0.222] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.054 | [0.038, 0.090] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.025 | [0.020, 0.030] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.016 | [0.015, 0.018] | |

Std. Dev. of | IG | 0.05 | 0.1 | 0.087 | [0.075, 0.104] | |

Deep habit in | B | 0.7 | 0.1 | 0.96 | [0.95, 0.97] | |

Adj. of habit stock of | B | 0.8 | 0.1 | 0.53 | [0.40, 0.63] | |

Deep habit in | B | 0.7 | 0.1 | 0.85 | [0.75, 0.92] | |

Adj. of habit stock of | B | 0.8 | 0.1 | 0.98 | [0.97, 0.99] | |

Price adj. cost | N | 17 | 5 | 48.90 | [43.6, 54.4] | |

Wage adj. cost | N | 100 | 30 | 102 | [92, 111] | |

γ | Preference parameter | N | 2 | 1 | 2.49 | [2.41, 2.58] |

Capacity util. parameter | N | 2.5 | 0.5 | 2.52 | [2.42, 2.68] | |

κ | Investment adj. cost | N | 2 | 0.5 | 1.99 | [1.84, 2.15] |

Int. rate smoothing | B | 0.8 | 0.2 | 0.60 | [0.54, 0.64] | |

Response of to | N | 1.6 | 0.2 | 1.67 | [1.52, 1.80] | |

Response of to | N | 0.1 | 0.05 | 0.09 | [0.07, 0.10] | |

Response of to | G | 0.5 | 0.25 | 0.017 | [0.011, 0.023] | |

Response of to | G | 0.5 | 0.25 | 0.020 | [0.012, 0.030] | |

Response of to | G | 0.5 | 0.25 | 0.009 | [0.005, 0.014] | |

Response of to | G | 0.5 | 0.25 | 0.439 | [0.227, 0.696] | |

Response of to | G | 0.15 | 0.1 | 0.148 | [0.105, 0.196] | |

Response of to | G | 0.15 | 0.1 | 0.132 | [0.073, 0.201] | |

Response of to | N | −0.05 | 0.05 | −0.039 | [−0.085, 0.006] | |

Response of to | N | −0.1 | 0.05 | −0.079 | [−0.162, 0.002] | |

ϕ | Corr. between and | N | 0.25 | 0.1 | 0.22 | [0.17, 0.25] |

### 4. ESTIMATION RESULTS

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

#### 4.1. Parameter Estimates

The mean and 5th and 95th percentiles of the posterior distribution for the parameters estimated are given in Table 2. All the shocks are significantly persistent. The preference parameter, investment adjustment cost, and capacity utilization parameters are estimated to be consistent with estimates in the literature.20 The degree of deep habit in private consumption is quite high, and the estimates for and suggest that the stock of habits for both public and private consumption depreciates slowly.

Quarter 1 | Quarter 4 | Quarter 12 | Quarter 20 | |
---|---|---|---|---|

NOTE ^{}These measure the present discounted value of the cumulative change in output over the present value cumulative change in the fiscal variable of interest over the *k*quarters. The reported numbers are the median multipliers, and the 95 percentiles are given below in brackets.
| ||||

Government Spending Multiplier | ||||

1.07 | 1.06 | 0.90 | 0.72 | |

[1.01, 1.13] | [0.96, 1.17] | [0.73, 1.07] | [0.49, 0.93] | |

Labor Tax Multiplier | ||||

0.13 | 0.32 | 0.68 | 0.85 | |

[0.09,0.18] | [0.22, 0.45] | [0.41, 1.09] | [0.42, 1.58] | |

Capital Tax Multiplier | ||||

0.34 | 0.43 | 0.52 | 0.46 | |

[0.30, 0.37] | [0.34, 0.51] | [0.30, 0.73] | [0.15, 0.81] |

The monetary policy parameters are estimated to indicate a high degree of interest rate smoothing and a significant response to inflation, satisfying the Taylor principle. Since monetary policy is active for the sample considered here, fiscal rule parameters are such that government debt is fully backed by future taxes, and spending and transfer decline in order for the equilibrium to be determinate and for the intertemporal government budget constraint to be satisfied. The tax rates are persistent and have a significant response to both the level of debt and output. Capital tax rates are found to be more responsive to the state of the economy than labor tax rates. Although there is evidence for automatic stabilization for taxes, government spending does not have a statistically significant countercyclical component. A discussion on the overall goodness-of-fit of the estimated model can be found in the online appendix.

#### 4.2. Transmission of Fiscal Shocks

Figures 1-4 show the impulse response functions as a result of shocks to the fiscal variables. The *x*-axis shows quarters after the shock hits the economy and the *y*-axis shows percentage deviations from the steady state. The impulse response functions are computed for randomly chosen 1,000 parameter draws from the Monte Carlo chains. The solid lines denote the median response and the dashed lines correspond to the 5th and 95h percentiles.

Figure 1 shows that in response to a 1% increase in government spending, output, consumption, hours, and wages rise, whereas investment falls with a delay. There are standard negative wealth effects that lead households to increase labor supply, which leads to a rise in output. There is a negative wealth effect on consumption as well, but since the model embeds deep habits in public and private consumption, an increase in government spending demand induces a decline in the markups. These variations in the markup shift the labor demand and, therefore, wages increase with output as a result of an increase in demand. This higher real wage causes individuals to substitute away from leisure to consumption, and this substitution effect is large enough to offset the negative wealth effect so that overall consumption rises in response to a government spending shock. However, these effects are short-lived since government spending is financed by a rise in distortionary taxes, which affects the marginal return on labor and capital. Investment does not move much on impact and slowly falls in response to a shock, primarily due to the rise in capital taxes.

The estimation is carried out using a full-information approach and fits the model to all the variation in the data, not just the dynamic effects of a spending shock. Even then, the responses of the variables are well in line with the literature on structurally identified VARs that study the effects of government spending shocks (see, e.g., Fatas and Mihov, 2001; Blanchard and Perotti, 2002). In particular, the model is in agreement with this literature in predicting positive responses of consumption and wages to a spending shock. The positive response of consumption, however, is small in magnitude and, as mentioned earlier, relatively short-lived in the model.

Figure 2 shows that in response to a 1% decrease in the labor tax rate, output, hours, consumption, and investment all rise. Wages fall on impact and then slowly rise above steady state. There is a positive wealth effect that results in consumption rising and labor falling, along with an intratemporal substitution effect leading to consumption rising further and labor rising due to a higher return on labor. This rise in labor supply results in wages rising in equilibrium. The cut in the labor tax rate also causes the return on capital to go up due to its effects on labor supply, leading to a rise in investment. Investment has a hump-shaped response due to investment adjustment costs. Also, note that since the degree of deep habit formation in private consumption is estimated to be high, it suggests households have a strong desire to smooth consumption, which also translates into a shift of demand from consumption to investment goods.

Figure 3 shows that a 1% fall in the capital tax rate results in hours, investment, and wages rising. Hours rise after a slight delay, and consumption has a small negative response. With a fall in the capital tax rate, the after-tax return on capital goes up, resulting in a rise in investment. Here the response of investment is once again hump-shaped and peaking at close to five quarters after the shock hits the economy because of investment adjustment cost. Intertemporal substitution effects lead agents to delay consumption and raise labor supply. However, wealth effects work in the opposite direction. In addition, capacity utilization goes up, as there is reallocation from labor to capital. These effects are generally similar to ones seen in standard neoclassical models (e.g., Braun, 1994). Looking at the equilibrium effects on consumption and labor, one has to take into account that soon after a fall in the capital tax rate, the labor tax rate rises and spending and transfers fall, to finance the deficit, and thus the consumption response is muted.

In both cases of a fall in labor and capital taxes, the model predicts a significant rise in investment. Although most of the literature does not tend to distinguish between capital and labor taxes, Blanchard and Perotti (2002), who identify a shock to total tax revenues in a SVAR, and Romer and Romer (2010), who identify tax shocks using a narrative approach, both also find significant crowding out of investment in response to a positive tax shock.21

Finally, Figure 4 shows that the responses to a 1% rise in lump-sum transfers are all insignificant on impact. The insignificant impact effect of transfers can be explained by the fact that in the absence of distortionary taxes, since this is a representative agent model, Ricardian equivalence would hold.22 Therefore a transfer is simply a negative lump-sum tax. The medium to longer run responses are driven by the rise in capital and labor taxes, which are used to finance this increase in transfers. Therefore, there is not a significant positive stimulative effect on output.

### 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

The stimulative effects of a fiscal action are generally framed in terms of multipliers. One measure is the impact multiplier, which is defined as the increase in the level of output *k* periods ahead in response to a change in the fiscal variable of interest given by at time *t*.23

So the spending impact multiplier is given by , and for the tax rates the impact multiplier is given in terms of the change in total tax revenues, so it is , where denotes tax revenues. The two tax shocks are normalized so that they result in a 1% decrease in total tax revenues.24

The impact multipliers, however, do not take into account that a shock at time *t* to tax rates or government spending results in a particular future path for the fiscal instruments given by the processes defined in the modeling section. To capture the cumulative effects of the fiscal shock along the entire path up to a given period, I follow Mountford and Uhlig (2009) and report the present value multiplier, which also discounts future effects.

gives the increase in present value of output over the next *k* periods as a result of a shock at time *t* to the fiscal variable of interest, *F*.

The present value multipliers are given in Table 2. The impact and present value multipliers take the same value in quarter 1, by definition. The present value tax multipliers build over time, whereas the spending multiplier decreases across the horizon. At longer horizons, tax and spending multipliers for output have the same magnitude. In fact, after close to five years, a cumulative one dollar decrease in tax revenues driven by labor tax cuts results in a one dollar increase in GDP and exceeds the stimulative effects of increased spending. Notice also that in terms of multipliers, labor tax cuts, although not as effective as capital tax cuts in the short run, boost output to a larger degree in the long run.

Table 3 shows the present value spending and tax multipliers for components of GDP, consumption, and investment. The spending multiplier for consumption is found to be positive but rather small in the short run, and in the long run it is negative. This positive multiplier for consumption is in line with structural VAR studies, in contrast to standard models that do not explicitly introduce a mechanism for public spending shock to transmit through the economy. The spending multiplier for investment is not significant in the first few quarters but becomes negative in the long run. The positive multiplier for consumption and the insignificant response of investment on impact also explain the size of the spending multiplier for output, being larger than 1. If, for instance, consumption and investment are both crowded out in response to a spending shock and have negative multipliers, then the resulting multiplier for output would be less than 1.25

Quarter 1 | Quarter 4 | Quarter 12 | Quarter 20 | |
---|---|---|---|---|

NOTE ^{}The reported numbers are the median multipliers, and the 95 percentiles are given below in brackets.
| ||||

Government Spending Multiplier | ||||

0.01 | 0.02 | 0.02 | 0.01 | |

[0.01, 0.02] | [0.01, 0.03] | [−0.00, 0.04] | [−0.03, 0.04] | |

−0.01 | −0.04 | −0.20 | −0.36 | |

[−0.06, 0.04] | [−0.15, 0.06] | [−0.41, −0.01] | [−0.67, −0.12] | |

0.65 | 0.62 | 0.54 | 0.48 | |

[0.62, 0.68] | [0.58, 0.68] | [0.48, 0.61] | [0.40, 0.55] | |

Labor Tax Multiplier | ||||

0.01 | 0.03 | 0.11 | 0.21 | |

[0.01, 0.02] | [0.02, 0.05] | [0.07, 0.18] | [0.12, 0.37] | |

0.11 | 0.27 | 0.57 | 0.69 | |

[0.08, 0.15] | [0.20, 0.38] | [0.37, 0.90] | [0.38, 1.26] | |

0.08 | 0.18 | 0.34 | 0.35 | |

[0.06, 0.10] | [0.13, 0.25] | [0.21, 0.53] | [0.17, 0.66] | |

Capital Tax Multiplier | ||||

−0.01 | −0.01 | −0.02 | −0.03 | |

[−0.01, −0.00] | [−0.02, −0.01] | [−0.03, −0.01] | [−0.06, 0.00] | |

0.08 | 0.16 | 0.24 | 0.23 | |

[0.05, 0.09] | [0.09, 0.21] | [0.10, 0.39] | [0.03, 0.46] | |

−0.06 | −0.02 | −0.03 | −0.12 | |

[−0.08, −0.05] | [−0.06, 0.01] | [−0.1, 0.04] | [−0.20, −0.02] |

Consumption has a small and positive multiplier in response to a labor tax shock on impact, which becomes larger at longer horizons. Conversely, the consumption multiplier is small and negative in response to a capital tax shock. Also, notice that the multiplier for investment in response to both tax shocks is sizable. This suggests that the expansionary effects of both labor and capital tax cuts on output are primarily driven by the stimulative effects on investment.

Table 3 also shows the multipliers for hours worked in the model, since the main motivation behind a fiscal stimulus plan is typically to boost demand and to raise employment.26 Employment has a significantly positive spending multiplier, which is largest on impact and slowly decaying over the horizon. This increase in hours worked, as a result of increased public spending, is due to a rise in both labor supply and demand. Labor supply shifts mainly because of households anticipating an increase in taxes, and price rigidities and countercyclical markups lead to a rise in labor demand of the firms with the shift in aggregate demand. The employment multiplier is also positive for labor tax cuts, and, whereas on impact the effects are small, they build significantly over time. These effects are primarily driven by the increase in labor supply due to the resulting higher return on labor. Unlike increased spending and labor tax cuts, capital tax cuts do not stimulate hours worked on impact. The multiplier for hours worked is insignificant for a range of 5–18 quarters after the shock hits the economy, and thus the effects are much smaller than the effects of alternative fiscal instruments.

There are some recent DSGE models where the effects of a spending shocks are estimated and spending multipliers can be inferred (see, e.g., Coenen and Straub, 2005; Lopez-Salido and Rabanal, 2006; Forni et al., 2009). These papers consider mechanisms to replicate the positive response of consumption to a spending shock, as suggested by VAR evidence, and find the spending multiplier in the range of 0.7 and 2. On the other hand, there has been no significant prior work done on estimating tax multipliers in a structural model.27

There is, however, a great deal of evidence in the VAR literature measuring the stimulative effects of spending increases and tax cuts. Studies employing structural VARs, such as Fatas and Mihov (2001), Blanchard and Perotti (2002), and Gali et al. (2007), also find output multipliers for spending close to 1.28 As mentioned earlier, these papers also find positive consumption multipliers. Blanchard and Perotti (2002) also emphasize the negative effect on investment of an increase in government purchases, which is seen in the model at longer horizons of 12 and 20 quarters. The slow rise in the stimulative effects of tax cuts is also documented in this literature, for example by Blanchard and Perotti (2002), Romer and Romer (2010), and Mountford and Uhlig (2009). Both Romer and Romer (2010) and Blanchard and Perotti (2002), though employing different identification schemes, also find that tax raises are highly contractionary primarily due to the effects on investment.

### 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

#### 6.1. Deficits versus Tax Financing

In the baseline model, government spending is financed by an increase in taxes and government debt. In this section, I evaluate the scenario where the government, relative to the historically estimated rules, is either more or less aggressively committed to retiring the debt. This is done in a manner similar to that in the exercise shown in Uhlig (2010), where the rate at which taxes respond to the level of debt is varied. More precisely, the processes for labor and capital tax rates are given as follows:

- (25)

- (26)

where corresponds to the baseline estimated rule. When γ is less than 1, then taxes are less responsive to debt and government spending is primarily financed by issuing debt. The values of correspond with taxes rising more aggressively in response to a deficit, and so government spending is financed by higher taxes than in the baseline case.

Figure 5 shows the present value spending multiplier for output at various horizons as γ is varied between 0.5 and 10, where 0.5 is the smallest value for which the equilibrium is determinate. In the short run, both the spending and tax output multipliers are generally unaffected, as taxes are overall slow to adjust to the rising level of debt. However, at longer horizons of 12 or 20 quarters, the multipliers become significantly smaller when taxes respond more aggressively to the level of debt in response to spending and tax shocks. In the case of tax shocks, because agents in the economy internalize that a tax cut today will be financed by aggressive tax increases in the future, the present value multipliers for longer horizons in fact become negative. Similarly, when , the longer run multipliers are much larger. Notably, the labor tax multiplier is as large as 1, exhibiting the sensitivity of longer run multipliers to tax financing.

Figure 6 shows the evolution of debt over a horizon of 20 quarters for varying degrees of γ in response to a government spending shock. Typically, debt takes as long as 50–100 years to come back to steady state. The slow evolution of debt has been documented by others, like Chung and Leeper (2007). After fiscal disturbances hit the economy, when γ is as high as 5 or 10, then debt returns to steady state in 5–15 years. In conclusion, although the multipliers are mostly unaffected at shorter horizons of up to a year, the method of financing, either by increased deficits or raising taxes, is important for longer run consequences.

#### 6.2. Lump-Sum versus Distortionary Taxation

A common assumption in the literature is exogenous fiscal policy with deficits financed by lump-sum taxes, which implies that Ricardian equivalence holds and the timing of the taxes does not affect the equilibrium. However, as pointed out in Baxter and King (1993), in a neoclassical model there are significant differences between government spending financed by changes in tax rates or changes in lump-sum transfers. The changes in lump-sum transfer payments are equivalent to debt financing when sequences for tax rates are fixed. In fact, in their calibrated model, there is a negative effect on output of an increase in government purchases when it is financed entirely by distortionary taxes. This is because of strong substitution effects on labor supply of tax rates.

In this section, the spending multiplier in the case of the estimated endogenous rules for tax rates are compared with the scenario when instead spending is financed by lump-sum taxes alone. This is done by shutting down the response of the distortionary taxes, by setting , and in addition setting so that government spending does not respond to the level of debt as well. There would be an increase in lump-sum taxes instead, since lump-sum transfers are the only fiscal instrument responding to the level of debt. This means that after an increase in government spending, while tax rates do not respond, lump-sum transfers adjust to ensure fiscal solvency and the return of the level of debt to steady state.

Figure 7 shows that the present value spending multiplier for output is consistently lower in the case of spending financed by distortionary taxes. Note, however, that the method of financing government spending, at least in the short run, does not have very significant effects. This is because, in the baseline model with distortionary taxes, the tax rates do not respond on impact and otherwise evolve slowly. Looking at the longer horizon, in the case of spending financed by lump-sum taxes, the multiplier is larger than one even close to 20 quarters, whereas in the estimated model with endogenous tax rates, the multiplier significantly decreases over time. This points toward careful consideration of conclusions about effects of fiscal policy in simpler models where government purchases are assumed to be financed entirely by lump-sum taxes, which is equivalent to deficit financing.

#### 6.3. Automatic Stabilizers

In this section, the role of the systematic response of fiscal instruments to the state of the economy is explored on the present value spending multiplier for output. These capture changes in government revenues and expenditures due to the changes in the state of the economy and do not require any discretionary action on the part of the government while playing the role of stabilizing fluctuations in the economy. This is done by varying the value of μ in the following processes:

- (27)

- (28)

- (29)

- (30)

Figure 8 reports the present value spending multiplier at different horizons for different values of μ. The automatic stabilizers take the estimated values when . In the case of a government spending shock hitting the economy, it raises output, which results in a rise in capital and labor tax rates and a decrease in transfers due to their countercyclical nature.

Now, when these stabilizers are larger, to dampen short-run fluctuations in the economy, the effects of an increase in government spending are reduced at all horizons, since the economy is stabilized by further increases in taxes and decreases in transfers. However, even though this is a short-run mechanism for mitigating the impact on demand, the effects in the long run are further exacerbated, as seen in the diverging present value multipliers at horizons close to 20 quarters.

### 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

In this section, I consider how the stance of the monetary policy affects the size of fiscal multipliers. The role of monetary authority is important in determining the movements of the real interest rate, which through intertemporal effects play a role in how macroeconomic variables react to fiscal shocks.

I start by exploring how the coefficients in the monetary policy rule affect the impact multiplier of output in response to government spending, capital, and labor tax shocks, shown in Figure 9. In the top panel, the nominal interest rate smoothing parameter, , is varied between 0.01 and 0.99, keeping the other parameters constant. The spending and capital tax multipliers for output rise with a higher value of , whereas the labor tax multiplier falls for higher values of the parameter. This is because in the case of spending and capital tax cuts, a higher value of means the monetary authority increases the real interest rate less rapidly, thus increasing the expansionary effects of these fiscal actions. In response to a labor tax cut, the model predicts a fall in inflation. Therefore higher values of imply that the desire to smooth interest rate strengthens in opposition to the downward pressure on interest rate due to effects of inflation.

The middle panel of Figure 9 shows that as the coefficient on inflation in the monetary policy rule, is perturbed, it does not significantly alter the impact multipliers in the case of increased government spending or reduced taxes overall. This is because inflation has a limited response to the fiscal shocks. However, notice also that as increases, the largest effect is on the impact labor tax multiplier, which decreases. This is because a labor tax cut causes households to increase labor supply due to a higher return on labor. This causes a fall in wages, and lower marginal costs results in a fall in inflation. Therefore, a larger response to inflation results in a smaller rise in the real interest rate, though these effects are small in magnitude.

The last panel shows that as the coefficient on output, , is varied between 0.04 and 0.5, the impact multipliers are significantly affected, particularly in the case of the government spending multiplier for output. As rises, the impact multiplier for output uniformly falls in the case of all fiscal shocks. If the nominal interest rate are highly responsive to the deviations of output from the steady state, then in the case of both spending and tax shocks, the nominal interest rate will rise sharply, causing the real interest rate to go up and a fall in aggregate demand.

The role of monetary policy is explored further by considering two extreme cases, one where the monetary authority is very aggressive in stabilizing both inflation and output ( = 2 and = 0.5), and the second where the monetary policy does not react significantly to variations in the state of the economy ( = 1.1 and = 0.02).29 Figure 10 shows the present value fiscal multipliers for output, consumption, and investment under these two rules and the estimated monetary policy rule. The *x*-axis shows the horizon in quarters.

The first row in Figure 10 shows the present value government spending multiplier. The multipliers for all components of demand are found to be larger than the baseline case under the accommodative monetary policy and smaller in the case of the aggressive monetary rule. In the estimated model, because markups are countercyclical, a government spending shock leads to an initial small decline in inflation, and inflation eventually rises once aggregate demand comes back to normal. The nominal interest rate responds significantly to both inflation and the rise in output, and overall this results in a rise in the real interest rate.30 In the case of aggressive monetary policy, the real interest rate rises more than the baseline scenario, which is primarily due to the strong response to deviations in output from the steady state. This leads to a fall in both consumption and investment demand in response to a government spending shock, and the output multiplier is less than 1, even on impact. Alternatively, in the presence of a relatively accommodative monetary policy, government spending has a higher stimulative effect on aggregate demand.31

The same effects are at play in response to a capital tax cut, as shown in the second row of Figure 10, so that an accommodative monetary policy results in a higher overall stimulative effects on output, consumption, and investment.

However, a less responsive monetary policy does not imply a larger stimulative effect in the case of all fiscal measures. The last row of Figure 10 shows the labor tax multiplier in the case of the estimated monetary policy rule, along with the two alternate rules. The labor tax multipliers for output, consumption, and investment are lower in the case of both new rules, relative to the estimated monetary policy rule. When and , since inflation falls in response to the cut in labor taxes, a smaller response to inflation results in a larger rise in the real interest rate than the baseline estimated model, causing components of demand to fall. In the case of and , the rise in the real interest rate is limited due to the large response to inflation, but because of the aggressive response to deviations of output from steady state, the overall real interest rate rises much more than in the baseline case. This once again results in a smaller multiplier in response to a labor tax cut.

In this section, I have shown that the stance of monetary policy has important implications for the size of fiscal multipliers. An accommodative monetary policy that has a limited response to inflation and output deviations results in higher overall stimulative effects of increased spending and capital tax cuts. This is, however, not the case for all fiscal measures, as shown for labor tax cuts. In this article, I consider the case of active monetary policy, since fiscal policy is estimated to be passive. Recent work by Cogan et al. (2010), Christiano et al. (2011), and Eggertsson (2010) provides supporting evidence to show that when the monetary policy is completely unresponsive or the nominal interest is at the zero bound, the monetary-fiscal interactions have significant effects on the size of fiscal multipliers.

### 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

In early 2009, the U.S. Congress passed a $787 billion package to stimulate the economy. The stimulus package comprises both increased government spending and tax cuts. In this section, the effects of the package on the economy are analyzed by simulating the implied changes in government spending and taxes in the estimated model.

To analyze the impact of increased spending contained in the stimulus package, note that two thirds of the bills goes toward public investment and government purchases and aid to state governments (60% of these transfers to states are used toward spending). Roughly a third of the package goes toward tax cuts, with the largest component in the form of payroll tax credits. In the model, these payroll tax credits can be thought of as a cut in the labor income tax rate.32

To simulate the American Recovery and Reinvestment Act of 2009 in the model, the path of government purchases from this stimulus package, as specified by Cogan et al. (2010), is introduced as a sequence of anticipated shocks into the economy.33 This means that in 2009:I, agents in the economy observe the entire path of expected government spending as shown in Figure 11. In addition, the tax cut is introduced as a 1% cut in labor income taxes in 2009:I.

The responses to both these shocks are computed in the model and are shown in Figure 11. The model predicts that the effects on GDP of the stimulus package would be most significantly felt during early 2010. There is a small increase in output initially as the households anticipate larger spending in the following years and, although the tax cuts are initialized in 2009, their effects take time to build, and the largest impact on GDP is a few quarters after the initial shock. Also notice that by late 2012, output multiplier is negative, even though government spending is still above steady state to stimulate the economy. This is because the agents are forward-looking and internalize that the large increase in spending is going to be financed by higher taxes. In fact, in response to the government spending stimulus alone, the consumption multiplier is negative starting mid-2010 because of households anticipating expenditures financed by higher taxes. It is also clear that this fiscal expansion comes with a large increase in the level of debt, which remains above steady state for many years. One caveat to note in this analysis is that this has not taken into account that the role of monetary policy under current circumstances is limited, as the Fed has been holding the nominal interest rate near zero.

### 9. CONCLUSION

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

This article provides evidence on the effects of fiscal policy actions in the context of a model featuring distortionary tax rates and rich fiscal rules, estimated using detailed fiscal data on tax rates, spending, and debt. I find that government spending has a large stimulative effect on impact, which decreases significantly at longer horizons. Tax cuts, on the other hand, are always less stimulative in the short run, but their effects build over time. In particular, the impact multiplier for government spending is 1.07, and the estimated model predicts a positive response of private consumption to government spending, which is in contrast to models that do not consider a channel of transmission of government spending shocks. The multipliers for labor and capital tax on impact are 0.13 and 0.34, respectively, which exceed the stimulative effects of increased spending at horizons of 12–20 quarters. These effects of tax shocks are primarily driven by the response of investment.

In addition, counterfactual exercises reveal that the speed at which government debt is retired following a fiscal shock has consequences for the stimulative effect of the fiscal policy action, and these are most important at longer run horizons. Furthermore, assessing the role of monetary policy, I find that the response of the monetary authority to deviations of output from the steady state is significantly important in determining the movements of the real interest rate. This, in turn, through intertemporal effects, has consequences for the size of fiscal multipliers. In fact, an accommodative monetary results in a higher fiscal multiplier for increased spending. However, less responsive monetary policy does not imply a larger stimulative effect in the case of all fiscal measures, as shown in the case of labor tax cuts.

- 1
- 2
Although deep habits have been explored in other smaller models to understand the propagation of public spending shocks in the economy (see, e.g., Zubairy, 2009; Ravn et al., 2012), in these studies the model is estimated using a limited information approach of matching impulse response functions to a policy shock.

- 3
Along with sticky prices, Gali et al. (2007) model noncompetitive behavior in labor markets and a fraction of the economy consisting of rule-of-thumb consumers who cannot borrow and save and consume their entire current income each period. In response to a government spending shock, price rigidities lead to a rise in wages, which causes credit constrained consumers to raise their consumption. If a large fraction of all consumers in the economy are assumed to be credit constrained, they get a positive response for aggregate consumption to a government spending shock.

- 4
One of the exceptions is Coenen et al. (2012), where almost all the different models considered also feature these liquidity constrained households.

- 5
In contrast to models based on the work of Gali et al. (2007), the fall in markup induced by deep habit formation is sizable relative to markup movements due to price stickiness. Therefore, there is no added assumption of an exogenously determined share of nonoptimizing agents needed.

- 6
Throughout the article, a hatted variable represents log deviations from its steady state.

- 7
Monacelli and Perotti (2008), in fact, also show this fall in the markup in response to a demand shock in the form of increased government spending, in a structural VAR.

- 8
The function introduces investment adjustment costs and has the following functional form: , and therefore in the steady state it satisfies and . These assumptions imply the absence of adjustment costs up to first-order in the vicinity of the deterministic steady state. The parameter κ is the investment adjustment cost coefficient.

- 9
In steady state,

*u*is set to be equal to 1, and so . During the estimation, is estimated, which determines dynamics. - 10
For sake of simplicity, I assume that the rate of depreciation used for tax purposes is the same as the physical rate of depreciation. However, Mertens and Ravn (2011) show that the distinction between the two might have a quantitative impact.

- 11
The fiscal rules are specified in terms of taxes and expenditures. However, these fiscal rules together with the government's budget constraint imply an evolution process of debt or deficit, which at times seems the main policy instrument in public debates.

- 12
The specification with all fiscal instruments responding to the level of debt has been shown by Leeper et al. (2010) to fit the data better in a model studying fiscal financing.

- 13
In this article all changes in fiscal instruments have been modeled as surprises, whereas in practise, many changes in spending and taxes might be anticipated. Work by Mertens and Ravn (2011) shows that pre-announced tax cuts result in a negative response of output on impact before the actual implementation, unlike a surprise tax cut. This suggests that the estimated tax multipliers might be biased by excluding this anticipation effect. However, including anticipated fiscal shocks would significantly increase the state variables of the model, and therefore this extension is left for future work.

- 14
The specific functional form of the production function is .

- 15
Modeling price stickiness via a quadratic cost leads to the same Phillips curve and dynamics up to first order as Calvo-Yun price stickiness.

- 16
The complete set of equilibrium conditions along with the steady state are given in the online appendix.

- 17
The data used in the estimation starts in 1958:1 due to the unavailability of property tax data prior to that date, which is used in the construction of capital tax data.

- 18
The diagnostics include trace plots, examining the autocorrelation functions, and CUSUM plots.

- 19
To further clarify the economic content of the priors, the online appendix also shows the fiscal multipliers implied by the priors.

- 20
The parameter estimates for the preference and capacity utilization parameters are similar to the prior, but robustness of these results was verified by estimating the model with different priors, but the posterior converges to very similar values.

- 21
Mertens and Ravn (2011) use the narrative approach of Romer and Romer (2010) to distinguish between anticipated and unanticipated tax shocks. The responses in the model are consistent with their findings regarding responses to unanticipated tax shocks. The only exception is the response of consumption to a capital tax shock, but unlike the case shown in this article, Mertens and Ravn (2011) consider the effects of capital tax shocks while restricting the reaction of labor taxes.

- 22
Recent work by Oh and Reis (2011) suggests that, for that reason, a representative agent model might not be suitable to study the effects of transfers on the economy and consider a model where Ricardian equivalence does not hold to look at the impact of targeted transfers.

- 23
For instance the government spending multiplier is computed as follows: , where

*Y*and*G*are the steady-state values of output and government spending, respectively. - 24
The estimated impact multipliers are shown in the online appendix.

- 25
This is true in the estimated DSGE model of Smets and Wouters (2007), which is not developed to study fiscal policy, as they do not consider a transmission mechanism for government spending shocks and assume spending financed by lump-sum taxes.

- 26
It might be worthwhile, however, to consider a model with search frictions in the labor market to fully explain the effects of fiscal shocks on labor, both at the extensive (employment) and intensive (hours per worker) margins.

- 27
An exception is Forni et al. (2009), who estimate both tax and spending multipliers for the Euro area.

- 28
Ramey (2011) employs a narrative approach, based on identifying episodes of large military buildups, and finds the maximum spending multiplier to be 1.1. Mountford and Uhlig (2009) use a sign restrictions approach to identify fiscal shocks and find the spending multiplier to be 0.65. These variations in the multipliers can be attributed to differences in identification schemes.

- 29
Note that and = 0.02 is the smallest reaction consistent with a determinate equilibrium in the estimated model.

- 30
Note that government spending shocks are more stimulative under less accommodative monetary policy; however, this effect would be even larger in the absence of deep habits, since in that case inflation would rise on impact in response to the positive spending shock.

- 31
Davig and Leeper (2011) also document similar interactions between monetary policy and the size of fiscal stimulus due to increased spending, where monetary policy determines the size of the implied intertemporal substitution effects arising in response to a spending shock and thus the ultimate response of components of aggregate demand. Their focus, however, is regime switching in both monetary and fiscal policy, and they characterize fiscal multipliers also in the regime where monetary policy is passive and fiscal policy is active.

- 32
Since, these payroll tax credits are close to 2% of the total tax revenues, and Blanchard and Perotti (2002) estimate the output elasticity of total tax revenues to be 2.08, this can be thought of as a 1% decrease in the tax rate. Uhlig (2010) also simulates this tax change as a 1% reduction in the labor tax rate.

- 33
Since the model has a feedback from output to government spending, some of the changes in spending might be attributed to automatic stabilizers and would not be a shock. It is important to notice though that the counter-cyclical component of government spending is estimated to be rather small. To verify whether automatic stabilizers are significant in this case, I simulate government spending for 2009:1, using data on GDP and spending in 2008, and do not find evidence of larger deviations of government spending from steady state relative to 2008. This suggests that the extraordinary increase in government spending introduced in the stimulus package is in fact discretionary fiscal policy.

### Supporting Information

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

Additional Supporting Information may be found in the online version of this article at the publisher's website:

### REFERENCES

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. MODEL
- 3. ESTIMATION
- 4. ESTIMATION RESULTS
- 5. THE ESTIMATED SIZE OF FISCAL MULTIPLIERS
- 6. COUNTERFACTUAL FISCAL POLICY EXPERIMENTS
- 7. SENSITIVITY OF FISCAL MULTIPLIERS TO MONETARY POLICY
- 8. SIMULATING THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009
- 9. CONCLUSION
- Supporting Information
- REFERENCES

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