The Impact of Government Spending on Private Spending in a Two-Sector Economy

Abstract

Based on evidence that the dynamics of private spending on durables seem to differ from that of nondurables and services, this article disaggregates the impact of an exogenous government shock into its effect on each type of consumption good. Different calibrations of a dynamic stochastic general equilibrium (DSGE) model suggest that increases in government spending crowd out private spending on durable goods, while they serve to expand nondurable and services spending. Vector autoregression (VAR) estimates across these sectors yield qualitatively similar results. The estimated responses are driven by a negative correlation between durable spending and two measures of government spending that has not greatly varied over time—whereas the correlation between nondurable spending and government consumption has remained consistently positive throughout the sample. Estimates are consistent with a Great Moderation in three components of consumption, whereas moderations in the volatility of government spending took place earlier than the 1980s. The Great Recession of 2008–2009 saw an increase in volatility of consumption spending with no similar increases in the uncertainty of government spending.

Keywords

government spending durable goods rule-of-thumb consumers Ricardian households DSGE TVP-VAR

Conventional wisdom anticipates that an increase in government spending has an expansionary effect on output. There is, however, no such agreement on the implied effect on consumption. Some predict that a rise in government expenditures precedes a decrease in consumption, while others argue the opposite.¹ Given that the dynamics of private spending on durables seem to differ from those of nondurables and services, it may be informative to disaggregate the impact of a fiscal shock into its effect on durables, nondurables, and services. For example, Greenwood, Hercowitz, and Krussell (1997) employed a two-sector model in which technology in the production of durable goods grows faster than in the rest of the economy. They argue that the official price deflators for durable equipment in the US National Income and Product Accounts (NIPAs) understate the relative price in sectoral rates of technological progress. Whelan (2003) argues that the fact that most investment spending is allocated to durable goods while most consumption spending is on nondurable goods and services is enough to reject the balanced growth prediction.

Real Business Cycle (RBC) proponents typically use as their canonical model a one-sector neoclassical growth framework that includes a consumption-leisure choice subject to some law of motion for the accumulation of the capital stock and some exogenous autoregressive process for aggregate technology. If this technology process results in aggregates that may be well characterized by a unit root process, then the ratio of any of the variables (the Great Ratios) will necessarily be stationary stochastic processes.² However, during the IT boom period, investment in real terms grew at an average 8.1 percent annually between 1991 and 2006, while consumption grew at an average 3.6 percent per year over the same period. Tevlin and Whelan (2001) disaggregate the data for the 1990s boom period to show that this increase in real NIPA investment in this period was entirely due to expenditures on producers’ durable equipment.

A substantive body of literature has estimated the effects of permanent and temporary fiscal-policy disturbances in macroeconomic aggregates.³ Given the evidence on the apparent different dynamics of durables versus nondurables, there may be important differences of the impact that fiscal policy disturbances have on each sector. This article measures the effects of changes in government purchases on private spending of durables and nondurables with a “what if” calibration exercise. This calibration allows for different behaviors of the representative agent. Given the unprecedented postwar level of explicit fiscal US stimulus that took place in 2008, the calibration excludes this unusual period.

Finally, an estimation is performed to include a postwar sample—which encompasses the Great Inflation, Great Moderation, and Great Recession periods. This estimation is carried out by means of standard vector autoregression (VAR) as well as a specification that allows for time variation (TV-VAR).⁴ This specification allows us to remain agnostic about the behavior of the agent. Thus, this estimation provides a counterpoint to the proposed calibration exercises. The introduction of time variation in the drift and the covariance of the TV-VAR has important advantages—as outlined in Keating and Valcarcel (2012)—not the least of which is that it lets the data speak for itself in ways that traditional VAR and DSGE models are typically ill equipped to do.

This article is motivated by the seemingly intractable debate regarding the implied fiscal effects on the largest component of aggregate demand. One of the reasons for the dispute on the direction of the response arises from the assumed behavior of the consumer. Proponents of the negative impact assume an infinitely lived Ricardian consumer who continually optimizes based on an intertemporal budget constraint. An increase in government spending reduces the value of after-tax income for these consumers who, under the stress of this negative wealth effect, will most likely cut her consumption.⁵ Proponents of a positive impact assume consumers behave in a non-Ricardian way, thus basing their consumption choice on their current disposable income and not their lifetime resources. For these consumers, the effect of an increase in government spending will depend crucially on how it is financed. According to Blanchard and Weil (2001), the total effect on output will depend on the extent of deficit financing and on the investment response.⁶

In order to empirically calculate these effects, this article presents a theoretical foundation that sufficiently describes the dynamics of private and public spending aggregate economic activity. A calibration that “nests” different assumptions of the behavior of the consumer is carried out. Then, an estimation that relies on a much weaker restriction of the parameter space is performed by means of a technique that allows the variance of different measures of government spending and different sectors of consumption to vary over time. I report consumption responses to a fiscal shock for the postwar period as well as predetermined subsamples across major events to elucidate whether the response has fundamentally changed during the Great Moderation period, the Great Recession period, or both.

The rest of this article is organized as follows. A Two-Sector Model with Two Consumer Types section presents the two-sector, two-consumer model and establishes equilibrium conditions. Empirical Application I: DSGE Calibrations section maps the theoretical model described in the previous section to a state space model by way of a complex generalized Schur decompositionand describes the calibration scheme and data. Empirical Application II: VAR Estimations section presents results from estimation procedures conducted by both a standard VAR and a TV-VAR and is followed by the Conclusion section.

A Two-Sector Model with Two Consumer Types

The economy consists of two types of consumers, a continuum of firms producing intermediate goods, a central bank carrying out monetary policy, a government authority in charge of fiscal policy, and a set of perfectly competitive firms producing two types of final goods. In this two-sector economy, sector 1 produces nondurable goods and services for consumption and structures for investment, while sector 2 produces durable goods and equipment that can be used by both consumers and producers.⁷ Omitting time subscripts, the production technology for each sector behaves according to⁸

Y_{i} = C_{i} + I_{i} + G_{i} = K_{1 i}^{β_{1}} K_{2 i}^{β_{2}} N_{i}^{1 - β_{1} - β_{2}}

for each sector i.

Equipment and structures are allowed to depreciate at different rates, so capital of both types (j) used in the production of sector (i) accumulates according to

K_{i j, t + 1} = (1 - δ_{j}) K_{i j, t} + I_{i j, t} .

A continuum of infinitely lived households with identical utility functions belongs to either of two types. The main difference between the two types of consumers is that one has access to capital markets, where a full set of contingent securities can be traded, and the other either has no access or chooses not to participate in the market for capital goods. I refer to the first type as the Ricardian consumers. These Ricardian consumers, who continually optimizes based on a budget constraint, trades and accumulates physical capital to rent out to firms. The second type does not accumulate any assets nor does he/she incur any liabilities but fully consumes his/her current labor income. I designate this consumer as rule-of-thumb consumers.⁹ There are myriad reasons for the rule-of-thumb consumer’s lack of participation in capital markets: lack of the precautionary saving motive, ignorance of intertemporal trading opportunities, lack of access to the market, and binding borrowing constraints, to name a few.

Given that Ricardian consumers are intertemporal optimizers, let $C_{t}^{o} a n d N_{t}^{o}$ represent the consumption and labor for these Ricardian optimizing households. This household’s objective is to draw leisure as well as consumption of both durables and nondurables and services. Thus, this household seeks to maximize

E_{0} \sum_{t = 0}^{\infty} {(\frac{1}{1 + ρ})}^{t} [α_{1} \log (D U_{t}) + α_{2} \log (C_{2t}^{o}) - \frac{N_{1,t}^{o}^{1 + ϕ}}{1 + ϕ} - \frac{N_{2,t}^{o}^{1 + ϕ}}{1 + ϕ}],

where the consumption shares and the Frisch marginal disutility of labor are all assumed nonnegative α₁, α_2, φ ≥ 0,¹⁰ subject to the sequence of budget constraints

- T_{t}^{o} + R_{t}^{k} K_{t}^{o} + B_{t}^{o} + D_{t}^{o} + W_{t} N_{t}^{o} \geq \frac{1}{R_{t}^{}} B_{t + 1}^{o} + P_{1, t} (C_{1, t}^{o} + I_{1, t}^{o}) + P_{2, t} (C_{2, t}^{o} + I_{2, t}^{o}),

along with a stock of durables (DU) kept by the household, which evolves according to

D U_{t} = (1 - δ_{U}) D U_{t - 1} + C_{1, t}^{o},

and the capital accumulation equation for each sector given by equation (2).

At the beginning of period t, consumers receives their labor income $W_{t} N_{t}^{o}$ , where W_t represents the real wage and $N_{t}^{o}$ the hours of work. $B_{t}^{o}$ is the endowment of nominally riskless one-period bonds carried over from last period, which pays one unit of the numeraire in the current period. R_t is the nominal return on bonds purchased in the current period. Consumers receive dividends ( $D_{t}^{o}$ ) from ownership of firms and income from renting their stock of capital ( $K_{t}^{o}$ ) to firms, which earns the real rental cost ( $R_{t}^{k}$ ). Finally, they pay taxes (or receives a transfer payment if negative) in the form of a lump-sum ( $T_{t}^{o}$ ). Their expenditures go to consumption ( $C_{t}^{o}$ ) and investment ( $I_{t}^{o}$ ) goods in each sector (in real terms). P _1t and P _2t denote prices of final goods for each sector.

Conversely, the rule-of-thumb consumers behave in a(n) (extreme form of) non-Ricardian fashion. These consumers, therefore, do not optimize intertemporally; they are assumed not to save or own firms and, therefore, they earn no dividends. Additionally, they do not own any stock of capital or monetary assets and, thus, do not rent out capital goods to firms or trade bonds. Given that they do not utilize any of the instruments typically used to smooth consumption, they make no attempts to stave off uncertainty in the fluctuation of their labor income, nor do they intertemporally substitute to adjust to variation in the interest rate. This household type will, therefore, seek to consume all disposable income net of taxes (which are allowed to differ from taxes paid by the optimizing consumer) as follows:

W_{t} (N_{1, t}^{r} + N_{2, t}^{r}) - T_{t}^{r} \geq P_{1, t} C_{1, t}^{r} + P_{2, t} C_{2, t}^{r} .

As with the Ricardian consumers, the stock of durables evolves according to the following constraint:

D U_{t} = (1 - δ_{U}) D U_{t - 1} + C_{1, t}^{r} .

The general budget constraint (equation 6) affects the rule-of-thumb consumers regardless of what sector they purchase from or supply to. The implication is that equation (6) reflects the combination of budgets under each sector and, therefore, a budget for either sector may be extrapolated. Thus, the budget constraint for the rule-of-thumb consumer in sector 1 yields a first-order approximation, around its steady state, of the rule-of-thumb household’s level of consumption for sector 1, as given by

c_{1, t}^{r} = \frac{W N_{1}^{r}}{C_{1}^{r}} [w_{t} + n_{1, t}^{r}] - (\frac{Y}{c_{1}^{r}}) t_{t}^{r},

with consumption, labor, and the real wage reflected in log deviations from their respective steady states and the deviation of lump-sum taxes measured as a share of steady state output.

The model includes a continuum of intermediate (j) firms supplying goods and services to final firms in either sector. Labor services hired by firm j ( $N_{x t} (j)$ in either x sector) can be imputed to some measure of aggregate labor demand for each sector ( $N_{x, t}$ ) in a straightforward way. Similarly, capital employed by each firm (j) can be aggregated to some measure of capital used to produce final goods in either sector.¹¹ Therefore, clearing of good and factor markets implies that the following conditions must hold for any period t in any given sector:

N_{i, t} = \int_{0}^{1} N_{i, t} (j) d j K_{i, t} = \int_{0}^{1} K_{i, t} (j) d j,

and

Y_{1, t} + Y_{2, t} = Y_{t} = C_{t} + I_{t} + G_{t},

where the aggregate resource constraint is the aggregate of each component across sectors and aggregate consumption, labor, investment, and capital in each sector are given by a convex combination of the corresponding variables for each consumer type in sector i:

C_{i, t} = λ C_{i, t}^{r} + (1 - λ) C_{i, t}^{o},

N_{i, t} = λ N_{i, t}^{r} + (1 - λ) N_{i, t}^{o},

and

I_{i, t} = (1 - λ) I_{i, t}^{o}, K_{i, t} = (1 - λ) K_{i, t}^{o},

where λ denotes the share of each consumer type. An infinitely large subset of monopolistically competitive firms is assumed to produce intermediate goods that are then used as inputs by firms producing final goods in either the nondurables and services or final durable goods sector.

A given producer of intermediate goods will employ labor as well as all types of capital available as inputs in order to supply to either sector, but not both.¹² The production function for a typical firm producing intermediate good i to be used as an input by a final producer in, say, sector 1 is given by

Y_{1, t} (i) = (K_{11, t} (i))^{β_{1}} (K_{21, t} (i))^{β_{2}} (N_{1, t} (i))^{1 - β_{1} - β_{2}},

where

N_{1, t} (i)

represents the labor services hired by firm i, while said firm employs

K_{11, t} (i)

nondurable goods and

K_{21, t} (i)

durables and services to supply

Y_{1, t} (i)

intermediate goods to a final firm producing in sector 1. A corresponding equation follows for the supply of intermediate goods to a final firm producing in sector 2.

The marginal product of labor dedicated to production in sector 1 is assumed to be identical to the marginal product of labor (MPN ₂ ) of those firms supplying to sector 2. This implies that the real marginal cost is common across all intermediate firms and given by the following:

M C_{t} = Ξ {(W_{t})}^{1 - β_{1} - β_{2}},

where

\frac{1}{Ξ} \equiv β_{1}^{β_{1}} β_{2}^{β_{2}} {(1 - β_{1} - β_{2})}^{1 - β_{1} - β_{2}}

Intermediate good firms in both sectors are assumed to follow Calvo’s (1983) staggered price setting model, with a fraction (η) of these firms leaving their prices unchanged in the current period. Each price has an equal probability of being adjusted in a given period. The intermediate goods firm resetting its price in period t will maximize

\underset{P_{t}^{*}}{M a x E_{t}} \sum_{k = 0}^{\infty} η^{k} E_{t} \{{(\frac{1}{1 + ρ})}^{k} (\frac{C_{t}}{C_{t + k}}) Y_{t + k} (i) ((\frac{P_{t}^{*}}{P_{t + k}}) - M C_{t + k})\},

subject to a sequence of demand constraints

Y_{t + k} (i) = {(\frac{P_{t}^{*}}{P_{t + k}})}^{- θ_{t}} Y_{t + k},

where

P_{t}^{*}

is the optimal price chosen by those firms that reset their prices at time t. The first-order condition associated with equation (14) is given by

\sum_{k = 0}^{\infty} η^{k} E_{t} \{{(\frac{1}{1 + ρ})}^{k} (\frac{C_{t}}{C_{t + k}}) Y_{t + k} (i) [(\frac{P_{t}^{*}}{P_{t + k}}) - μ^{P} {M C}_{t + k}]\} = 0,

where

μ^{P} \equiv \frac{θ_{t}}{θ_{t} - 1}

is the gross price markup prevailing in a zero-inflation steady state in the absence of frictions.¹³ Market clearance for sector 1 implies

Y_{1, t} = C_{1, t} + I_{11, t} + I_{12, t} + m G_{t}

, where mindicates the share of total government expenditures allocated to durable goods.

The finished goods-producing firm maximizes its profits by choosing the following set of demand schedules:

Y_{t} (i) = {(\frac{P_{t} (i)}{P_{t}})}^{- θ_{t}} Y_{t},

where Y_t (i) describes the amount of intermediate good i used as an input by the final goods firm in either sector. The parameter θ _t measures the time elasticity of demand for each intermediate good, and thus, it constitutes a markup. Some researchers include it as a cost push shock in the model’s Phillips curve relationship.¹⁴ The equilibrium zero-profit condition that determines the aggregate price level P_t follows the well-known Dixit-Stiglitz price (1977) index is

P_{t} = {[\int_{0}^{1} P_{t} (i)^{1 - θ_{t}}]}^{\frac{1}{1 - θ_{t}}} .

As with the intermediate goods-producing firm, the final firms are assumed to be identical ex ante across sectors with the exception of the differentiated good they produce, which again can be sold as a nondurable, service, or durable good.¹⁵

The optimal reset price for a final goods-producing firm may be expressed as

P_{t}^{*} = (1 - \frac{1}{1 + ρ} η) \sum_{k = 0}^{\infty} {(\frac{1}{1 + ρ} η)}^{k} E_{t} \{m c_{t + k}^{n}\},

where

m c_{t}^{n}

is the nominal marginal cost for the final goods-producing firm at time t. This optimal reset price implicitly encompasses the case of perfect flexibility

(θ_{t} = 0)

where the firm adjusts its price proportionately to movements in its current marginal cost, as well as the case of price rigidities

(θ_{t} > 0)

, where the future becomes relevant. From these rules, it is possible to derive an inflation equation of the following form:

π_{t} = ξ m c_{t} + \frac{1}{1 + ρ} E_{t} \{π_{t + 1}\} .

Monetary policy is carried out by a central bank that is assumed to set nominal interest rates every period according to the simplified Taylor rule:¹⁶

r_{t} = r + ϕ_{π} π_{t} .

ϕ_{π} > 1

in this linear interest rate rule (equation 19), an increase in inflation will ultimately lead to a more than one-for-one increase in the nominal interest rate. This condition is necessary and sufficient to guarantee the uniqueness of equilibrium¹⁷ in the absence of rule-of-thumb consumers.

Government inflows come from the usual sources: tax revenues and loans to both consumers and firms. Total tax revenue in any given period is given by a convex combination of taxes paid by Ricardian and non-Ricardian consumers so that $T_{t} \equiv λ T_{t}^{o} + (1 - λ) T_{t}^{r}$ . The second source of revenue comes from selling bonds in the open market. Government spending comes from spending as well as liquidating government debt. One of the main motivations of this study is to determine the effects fiscal policy has had on different types of consumption in the United States. Unless government seeks to run a deficit in some given period, expenditure must be no larger than tax revenues in the current period and whatever debt was incurred last period. Consequently, by normalizing government budget constraint with the steady state deviations of government expenditures, taxes, and bonds by steady state output, the following fiscal policy rule ensues:

t_{t} = ϕ_{b} b_{t} + ϕ_{g} g_{t} .

Finally, government purchases fluctuate exogenously according to the following stationary autoregressive process:

g_{t} = ρ_{g} g_{t - 1} + ϵ_{t},

where

0 < ρ_{g} < 1

and the independently and identically distributed (i.i.d) government spending shock

ϵ_{t}

has a constant variance

σ_{ϵ}^{2}

Empirical Application I: DSGE Calibrations

A linear expectation system of difference equations of the form (equation 22) can be derived from the equilibrium conditions for the consumer and the producer that are obtained from the construct specified in the previous sections.

A E_{t} \{x_{t + 1}^{0}\} = B x_{_{t}}^{0} + C υ_{t},

where

x_{t} \equiv [n_{1, t}, n_{2, t}, c_{1, t}, c_{2, t}, k_{1, t}, k_{2, t}, π_{t}, b_{t}]

. The elements of matrices Aand B are populated by the underlying structural parameters. This system can be identified by uncoupling the unstable and stable components and then solving the unstable components forward and the stable component backward. One algorithm that accomplishes this is the one outlined by Klein (2000). Klein’s method is based on the complex generalized Schur decomposition. In order to arrive at a just-identified system, the long-run restrictions implied by the model’s equilibrium conditions are supplemented with an initial guess on some of the parameter values. Once the system is identified, it can be allowed to be driven by the exogenous government shock of equation (21) under different calibrations of the parameters of interest.

The following calibrations allow for different assumptions about consumer behavior and prices. Some of the following values that may be common to both specifications are fixed a priori. For example, the discount factor is set to 0.99,¹⁸ the elasticity of capital with respect to output is set to 0.31, and the rate of depreciation of durable capital goods and stocks of nondurable goods are assumed to be 0.13 and 0.03, respectively.¹⁹ I follow King and Rebelo’s (1999) average value of 0.065 for the rate of return on capital and Rotemberg and Woodford’s (1999) elasticity of wages with respect to output of 0.3.²⁰ All these parameter values remain constant in the calibrations that follow.

Next, I turn to those parameters that are allowed to change in the calibrations to allow for the possibility of different specifications. The wedge between the marginal rate of substitution and the marginal product of labor can be interpreted as a price markup. I assume the steady state price markup $(μ^{p})$ equal to 0.2, a value suggested by Galí, Lopez-Salido, and Valles (2004). The baseline weight for Ricardian $(1 - λ)$ and non-Ricardian (λ) households is also set to one-half.²¹ The magnitude of the response of the central bank to inflation $(ϕ_{π})$ is set to 1.5, a standard value in empirical Taylor rules. I follow the methodology in Galí, Lopez-Salido, and Valles (2004) to pin down parameters of the fiscal policy rule (equation 20) as well as government spending (equation 21) where the government shock is assumed to be not explosive but highly persistent so $ρ_{g} = 0.9$ . The share of government spending (m) on durables is set around 0.33.

Using US quarterly data, I calibrate the response of several macroeconomic variables to a government spending shock. The proposed model has implications for several observables including a measure of government spending, consumption of durables, consumption of nondurables and services, hours worked in production in each sector, private nonresidential investment, private residential investment, inflation, and the budget deficit.²²

As mentioned in the previous section, I calibrate a model with New Keynesian characteristics that allows for a mix of “rule-of-thumb” and optimizing consumers, a wedge between the marginal rate of substitution and the marginal product of labor of the household, and the degree of annualized price adjustment. Thus, in what I dub the benchmark calibration, I allow for an even mix of consumer types by setting $λ = 0.5.$ Additionally, I set the share of firms that keep their prices unchanged $η = 0.75$ , which corresponds to an average length of sticky prices of one year. Finally, I follow Galí, López-Salido, and Vallés (2005) in setting the steady state markup $μ^{p}$ equal 0.2.

Figure 1 shows the responses by sector of an increase in government spending in the benchmark model. Both consumption of durable and nondurable goods see an increase following the positive shock to government spending.

As a means of comparison, I then simulate the effect of a government shock in the context of an RBC view. To that end, I consider the following: all consumers are optimizers, so I set the share of rule-of-thumb consumers in the economy (λ) to zero. I allow the price-staggering scheme to vanish by setting the share of firms that keep their prices unchanged $(η)$ to zero. Finally, to allow for perfect market flexibility, I do away with the wedge $μ^{p} = 0$ . Hence, this specification assumes that households intertemporally optimize subject to their resource constraints in a perfectly competitive market with no rigidities. The effects are reflected in figure 2.

The positive fiscal shock leads to a small decrease in consumption of durables. According to this calibration, with the economy populated by optimizing households and characterized by fully flexible prices, consumption of nondurable goods rises following a positive fiscal shock. This evidence is in sharp contrast with the RBC prediction of a crowding out effect of government spending and more in line with the New Keynesian theoretical prediction as well as the evidence from figure 1. This result of an increase in nondurable consumption following a fiscal expansion is robust to both specifications.

Figure 3 displays responses consistent with a rather strict representation of a New Keynesian view. This calibration allows for the presence of stickiness in an economy solely populated by non-Ricardian consumers. Here as well, consumption in both sectors increases following the exogenous fiscal shock. Hence, the effect on nondurable consumption does not seem to be sensitive to the assumed behavior of the consumer or the presence of nominal rigidities in the economy since all calibrations considered are robust to an unambiguous increase in nondurable spending following the fiscal shock. Thus, the qualitative difference between the two views seems to be reduced to a debate on the response of durable spending to an exogenous government increase. The benchmark and Keynesian calibrations predict an increase in consumption in the durables sector. The RBC calibration predicts a negative response of durables to the fiscal shock. This is consistent with the crowd-out theoretical prediction in those models. Importantly, nondurable disbursements and services spending in the United States are larger than the gross amounts of annual spending on durables; hence, it is reasonable to expect this decrease in durable spending—as predicted by the RBC calibration—to be overshadowed by a predicted nondurable spending increase in a traditional one-sector model.

These results underscore the importance of considering durable goods—separately from the rest of the economy—to draw inference on the dynamics of various aggregates when subjected to exogenous fiscal shocks. Barsky, House, and Kimball (2007) make the case for carefully considering durable spending when the economy is subjected to monetary shocks. They argue that it is the longevity of durable goods that elicits important differences in the dynamic responses of monetary models. These dynamics would otherwise remain hidden if the production or consumption of durable goods is not explicitly specified. They argue that the stock of durables is nearly constant over the time span during which monetary shocks might have real effects. This implies that the intertemporal elasticity of substitution for durables spending should be naturally high. Thus, even modest changes in relative prices can lead to pronounced swings in the production of these goods.

Rule-of-thumb behavior by some households (who in this model are assumed to fully deplete their current labor income every period) and price rigidities, as those assumed in the New Keynesian literature, are often pointed out to constitute this positive response of private consumption to public spending increases.²³ While these fiscal expansions would necessarily lead to increased taxation today or tomorrow, rule-of-thumb consumers may not internalize this as a negative wealth effect. Thus, this nonoptimizing behavior “desensitizes” aggregate demand from the perceived negative wealth effect. Additionally, in the presence of sticky prices, the price markup may correct downward enough to lead to increases in the real wage even when faced with a drop in the marginal product of labor. The difference in the quantitative and the qualitative response between the two sectors across specifications, again, would seem to lie with the behavior of the consumer. While a substantial intertemporal substitution drive can be associated with the consumption of large-ticket items, nondurable spending is likely subject to the consumption-smoothing logic of the permanent income hypothesis. Importantly, the robustness of the positive effect on durable consumption between the widely different assumptions of the two views argues for the necessity of modeling the economy with two sectors.

Empirical Application II: VAR Estimations

As a means of sensitivity analysis, this section describes results from an unrestricted VAR in order to elucidate whether the effects of government spending on the consumption of durables is different from that of nondurables and services. Standard VAR approaches have been popular in estimating the effects of fiscal shocks (see Blanchard and Perotti [2002] as a notable example).²⁴ Given the evidence of a substantial reduction in the volatilities of US aggregates beginning around 1984 (see McConnell and Perez-Quiros [2000], and Stock and Watson [2002] among many others) in addition to evidence that this Great Moderation in US economic activity may be over (Clark 2009; Valcarcel 2012),²⁵ it might be of interest to investigate whether these substantial changes in volatility have changed the impact of the responses of aggregates to, say, fiscal shocks. To that end, this section reports posterior estimates of the volatilities of—and the time-conditional correlations between—government spending and consumption. It also shows the overall consumption response to exogenous government shocks and whether the response has fundamentally changed since 1984, and then again since 2007.

Figure 4 shows estimates (from the same TV-VAR) of the time-varying correlations among two measures of government spending: government consumption spending (GCS) and government nondefense investment (GNDI) and three measures of consumption spending—durable, nondurable, and services spending. These (along with posterior standard deviations in figure 5) are computed following a TV-VAR methodology described in Keating and Valcarcel (2012). A clear picture emerges from these charts. While nondurable spending seems to have been positively related to government spending, durable spending has consistently been negatively correlated with government spending throughout the sample. The correlation between government spending and services is less clear. Government consumption and services spending have nearly always been positive until the mid-2000s when the correlation turns negative, whereas the time-varying correlation between nondefense investment and services has flipped from positive to negative throughout the sample.

Figure 5 shows estimates of the posterior standard deviations of various measures of government and consumption spending. Inspection of this chart suggests that while the volatility of durable, nondurable, and services spending reduced substantially in the mid-1980s—consistent with the Great Moderation—the volatility reduction in GCS is more gradual and protracted over the whole sample and that the volatility reduction in GNDI takes place earlier, around the early 1970s. The Great Recession period of 2008–2009 shows increasing volatilities in services and, especially, nondurable consumption—which, combined, comprise a substantial portion of gross domestic product (GDP). This increase in volatility in the largest component of GDP is consistent with the post-2007 increase in the uncertainty of economic activity that Clark (2009) and Valcarcel (2012) find.²⁶

Figure 6 shows that both services (figure 6a) and nondurable consumption spending (figure 6b) increase following an exogenous shock in government consumption. The response of nondurable spending does not seem to have experienced a fundamental change during the Great Moderation (see figure 6d) or Great Recession periods.²⁷ Conversely, the magnitude of the response of services spending to an exogenous government spending shock is substantially larger (see figure 6c) in the pre–Great Moderation period, before 1984, than afterward. This difference in the magnitude of the response is statistically significant at two standard deviations. Services spending shows a very small negative—but not statistically significant—response to a government shock during, and immediately after, the Great Recession period. This suggests that the massive fiscal stimulus package associated with the American Recovery and Reinvestment Act of 2009 had relatively little effect on services spending.

In contrast with the positive response of nondurables and services to shocks in government spending, figures 6e through 6h suggest a decrease in durable spending following an exogenous government spending shock, whether it be a shock to government consumption, as can be seen in figure 6e, or nondefense investment as denoted by figure 6f. The negative effect of government spending on durables is consistent with the predicted negative correlation between the two from the earlier mentioned TV-VAR and do not seem to behave differently across the 1984 imposed break. Estimates from the standard VAR, the TV-VAR, and the calibrated DSGE models all seem to point to a crowding-out effect of government spending on private spending of durable goods.

Conclusion

The debate that centers on the impact of public spending on private spending rages on. Two schools of thought, which predict a diametrically opposite effect of public spending on private consumption, differ in household behavior and price flexibility assumptions but base their theoretical foundation on a single-sector economy. Hinged on empirical evidence of differences in the dynamics in spending on long-lived assets relative to the rest of the economy, this article constructs an economy populated by two sectors: one engaged in the production of durables (which mostly go to investment spending) and one that produces nondurable goods (which mostly go to consumption). In addition, two types of consumers exist in this economy: those who intertemporally optimizes their labor utility subject to their resource constraints and those who myopically consumes all of their current labor income. Finally, a dimension of price rigidity, based on the Calvo price staggering system, is considered. A benchmark model that allows for an even mix of rule-of-thumb and optimizer consumers along with the presence of sticky prices in a two-sector economy is considered. A second model, consistent with an RBC approach, features infinitely lived optimizer consumers in a two-sector market with flexible prices. A third toy economy entirely populated by rule-of-thumb households and staggered price-setting firms is also considered. The consideration of durable goods consumption—as a separate sector from the rest of the economy—is central in these calibrations and distinguishes this article from the traditional one-sector models typically considered for analyzing fiscal policy. This framework generates a positive relationship between consumption of nondurables and government spending, which is robust to different specifications of household behavior and price stickiness. The effect on durable consumption, however, follows the theoretical predictions of the two views considered. Given that, annually, nondurable disbursements and services spending in the United States are larger than spending on durables, one would expect that this decrease in durable spending—as predicted by the RBC calibration of the two-sector model—would be overshadowed by a predicted nondurable spending increase in a traditional one-sector model. Hence, by disaggregating private spending between durable spending relative to the rest of consumption spending, we may uncover important insights on the fiscal effects on private spending that would otherwise remain hidden in traditional one-sector models.

Different assumptions about consumer behavior, access to capital markets, and price rigidities are typically advocated to as the basis for the opposite prediction of the effects of the fiscal shock on consumption. This article suggests that none of these factors seems to be very important in driving the response if one focuses on aggregate consumption. Important differences in the consumption response to a fiscal shock are overshadowed by the larger share of consumption that goes to nondurables and services. Different calibrations of a DSGE model as well as a standard VAR and TV-VAR suggest that government spending crowds out private spending on durable goods, while it serves to expand nondurable and services spending. These dynamics are consistent with the estimated time-varying correlations of figure 4. Durable spending seems to be negatively correlated with government spending while nondurable spending is positively correlated with government spending throughout the sample. These correlations do not seem to exhibit large swings around the 1970s–1980s and the late 2000s. These periods, however, are characterized by important changes in the volatility of these aggregates. Estimates of the TV-VAR show the Great Moderation affects all three consumption sectors. Both government consumption and nondefense investment also moderate in this period, but the reduction pales in comparison with much deeper volatility decreases that occur earlier in the sample—in the 1960s and mid-1970s for government consumption and mid-1960s for government nondefense investment. Finally, the 2008–2009 Great Recession period sees an increase in volatility of services and an even more important increase in nondurable consumption. Remarkably, while the volatilities of consumption and government spending underwent important changes in the postwar period, the correlations among those variables—as well as the magnitudes of the durable and nondurable responses to exogenous fiscal shocks—have remained relatively stable. The positive response of services spending to a fiscal shock has reduced in a statistically significant way since the Great Moderation.

Overall, this article uncovers a diametrically opposed dynamic in the sectoral consumption response to a fiscal shock based both on a calibrated DSGE model that is highly stylized and a VAR estimation that allows for little restriction of the parameter space. Government spending seems to generally induce a positive response in nondurable and services spending. This would suggest that fiscal stimulus may have a positive impact on spending in small ticket and first necessity items. The response of durable spending to government spending goes in the opposite direction. This response is consistent with the crowding-out effect that government spending exerts on private spending on large ticket items and goods that typically go to investment, such as durable spending.

This article conducts a parsimonious analysis in order to center on the key point of inquiry of this debate. For tractability, it abstracts from a number of possible extensions. For instance, this theoretical analysis assumes the simulated increase in public spending to be financed with lump-sum taxes. Allowing for distortionary taxes will likely lead to different conclusions that will depend on the timing and composition of the taxation. Opening the economy to trade would likely yield further insights in the composition of the response from either sector to the increase in government spending considered here. Another extension that could prove beneficial would be to incorporate some form of rigidity in setting the nominal wage. This would likely have a significant effect on the marginal product of labor and, thus, labor income and consumption to a fiscal shock. Finally, allowing for technology shocks—to act as direct competitors with the fiscal shocks assumed here—could elicit a different response from both sectors, which might yield further insights on the importance of fiscal shocks for fluctuations in private spending.

Footnotes

Acknowledgment

The author would like to thank John Keating, Peter Summers, Shu Wu, Shigeru Iwata, Ted Juhl, Ron Gilbert, Brandon Dupont, and MEG and MVEA conference participants for their helpful comments. The usual disclaimers apply.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Aiyagari

Rao

Christiano

Lawrence

Eichenbaum

Martin

. 1990. “Output, Employment and Interest Rate Effects of Government Consumption.” Journal of Monetary Economics 30:73–86.

Barsky

Robert

House

Christopher

Kimball

Miles S.

. 2007. “Sticky Price Models and Durable Goods.” The American Economic Review 97:984–98.

Baxter

Marianne

King

Robert

. 1993. “Fiscal Policy in General Equilibrium.” The American Economic Review 83:315–34.

Blanchard

Olivier

Perotti

Roberto

. 2002. “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” Quarterly Journal of Economics 117:1329–68.

Blanchard

Olivier

Weil

Philippe

. 2001. “Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty.” Advances in Macroeconomics 1 (2), Article 3:1–21.

Calvo

Guillermo

. 1983. “Staggered Prices in a Utility Maximizing Framework.” Journal of Monetary Economics 12:383–98.

Christiano

Lawrence

Eichenbaum

Martin

. 1992. “Current Real Business Cycle Theories and Aggregate Labor Market Fluctuations.” The American Economic Review 82:430–50.

Clark

Todd E.

2009. “Is the Great Moderation Over? An Empirical Analysis.” Economic Review, Federal Reserve Bank of Kansas City 94:5–42.

Fatas

Antonio

Mihov

Ilian

. 1999. “The Effects of Fiscal Policy on Consumption and Employment: Theory and Evidence.” Center for Economic Policy Research. Discussion Papers 2760.

10.

Galí

Jordi

López-Salido

David

Vallés

Javier

. 2004. “Rule-of-Thumb Consumers and the Design of Interest Rate Rules.” The Journal of Money, Credit and Banking 36:739–63. Conference Commemorating the 35th Anniversary of the Publication of James Tobin’s Paper “A General Equilibrium Approach to Monetary Theory.”

11.

Galí

Jordi

López-Salido

David

Vallés

Javier

. 2005. “Understanding the Effects of Government Spending on Consumption.” Journal of the European Economic Association 5(1):227–70.

12.

Greenwood

Jeremy

Hercowitz

Zvi

Krusell

Per

. 1997. “Long-Run Implications of Investment-Specific Technological Change.” The American Economic Review 87:342–62.

13.

Ireland

Peter

. 2002. “Technology Shocks in the New Keynesian Model.” NBER Working Paper 10309, National Bureau of Economic Research, Inc.

14.

Kaldor

Nicholas

. 1957. “A Model of Economic Growth.” Economic Journal 67:591–624.

15.

Katz

Arnold J.

Herman

Shelly

. 1997. “Improved Estimates of Fixed Reproducible Tangible Wealth, 1929-1995.” Survey of Current Business 75:69–92.

16.

Keating

John W.

Valcarcel

Victor

. 2012. “Greater Moderations.” Economics Letters 115(2):168–71 .

17.

King

Robert G.

Plosser

Charles I.

Stock

James H.

Watson

Mark

. 1991. “Stochastic Trends and Economic Fluctuations.” The American Economic Review 81:819–40.

18.

King

Robert G.

Rebelo

Sergio T.

. 1999. “Resuscitating Real Business Cycles.” In Handbook of Macroeconomics, vol. 1, edited by Taylor

J. B.

Woodford

, 927–1007. Amsterdam: Elsevier.

19.

Klein

. 2000. “Using the generalized Schur form to solve a multivariate linear rational expectations model.” Journal of Economic Dynamics and Control 24: 1405–23.

20.

Mankiw

Gregory

. 2000. “The Savers-Spenders Theory of Fiscal Policy.” The American Economic Review 90:120–25.

21.

McConnell

Margaret M.

Perez-Quiros

Gabriel

. 2000. “Output Fluctuations in the United States: What Has Changed Since the Early 1980s?” American Economic Review 90:1464–76.

22.

Rotemberg

Julio

Woodford

Michael

. 1999. “The Cyclical Behavior of Prices and Costs.” NBER Working Papers 6909, National Bureau of Economic Research.

23.

Stock

James

Watson

Mark

. 2002. “Has the Business Cycle Changed and Why?” NBER Macroeconomics Annual 17:159–218.

24.

Tevlin

Stacey

Whelan

Karl

. 2003. “Explaining the Investment Boom of the 1990s.” The Journal of Money, Credit and Banking 35:1–22.

25.

Valcarcel

Victor

. 2012. “The Dynamic Adjustments of Stock Prices to Inflation Disturbances.” Journal of Economics and Business 64(2):117-44 .

26.

Whelan

Karl

. 2003. “A Two-Sector Approach to Modeling U.S. NIPA Data.” The Journal of Money, Credit and Banking 35:627–56.

27.

Woodford

Michael

. 2003. Interest and Prices. Princeton, NJ: Princeton University Press.