Government Spending and Consumption at

the Zero Lower Bound: Evidence from

Household Retail Purchase Data∗

Bill Dupor

Federal Reserve Bank of St. Louis

Marios Karabarbounis

Federal Reserve Bank of Richmond

Marianna Kudlyak

Federal Reserve Bank of Richmond

M. Saif Mehkari

University of Richmond

February 15, 2016

PRELIMINARY- PLEASE DON’T CIRCULATE

Abstract

This paper uses cross-regional variation in the fiscal stimulus of 2009-2013 to analyze the

effects of government spending on household-level consumption when the nominal interest rate

is zero. The key novelty is the construction of a comprehensive measure of local consumption

expenditures using (i) household-level retail purchase data using Nielsen Homescan Consumer

Panel and (ii) state-level consumption data from the BEA. Most of our specifications point

toward a significantly positive consumption multiplier around 0.25 for non-durable consump-

tion. We translate our regional multiplier into an aggregate multiplier using a heterogeneous

agents, New Keynesian model with multiple regions and input linkages.

∗Emails: Bill Dupor: billdupor@gmail.com; Marios Karabarbounis: marios.karabarbounis@rich.frb.org;Marianna Kudlyak: marianna.kudlyak@rich.frb.org; M. Saif Mehkari: smehkari@richmond.edu

1 Introduction

Does government spending reduce of enhance private consumption spending? Empirical

estimates of the effect of government spending on consumption vary greatly. Blanchard and

Perotti (2002) find a positive effect while Ramey and Shapiro (1998) find that during episodes

of large exogenous increases in defense spending, private consumption falls.

More importantly, there is no empirical work on the effect of government spending on

consumption at periods when the nominal interest rate is at the zero level. During such

periods government spending can have big effects by increasing expected inflation and over-

stimulating consumption (Christiano, Eichenbaum, and Rebelo, 2011). Resorting to standard

VAR/event techniques would not suffice as periods of zero nominal interest rates are very few

and they usually not coincide with periods of large military expansion.

This paper sets up a novel exercise to tease out the effect of government spending on

consumption when the economy is at the zero lower bound. The key innovation is the con-

struction of a comprehensive measure of consumption expenditures at the local level using (i)

household-level retail purchase data from the Nielsen Consumer Panel Data and (ii) state-level

consumption data from the Bureau of Economic Analysis. We then merge our consumption

measures with local measures of government spending from the American Reinvestment and

Reenactment Act and exploit the regional variation in government spending during the period

2009-2013. To our knowledge this is the first paper to use cross-regional variation to study the

effects of government spending on consumption. Our data allows us to focus on a period when

nominal interest rates were zero and hence speak empirically to the literature of government

spending at the zero lower bound.

Our cross-regional analysis points towards significantly positive effects of government

spending on consumption at all levels of aggregation. Based on our household-level con-

sumer data, households in counties that received an additional dollar spent between $0.04

and $0.35 for retail purchases relative to households in counties that did not receive any aid.

Households in states that received one more dollar, spent between $0.20 to $1.31 in retail pur-

1

chases. Our aggregated state-level data provide estimates in the same range for non-durable

consumption. In particular, states that received one more dollar in government aid, spent on

average between $0.22 to $0.32.

Our estimates for durable consumption expenditures are less robust. Some specifications

point toward significantly positive effects: states that received one more dollar in government

aid, spent on average between $0.30 to $0.65 for durable purchases. For other specifications

the durable consumption effects are small and insignificant. The quality of our data allows us

to study jointly multiple levels of aggregation (zip code, county, and state) and analyze the

effect of government spending on different income groups.

A major challenge in our analysis is to address the endogeneity between government aid

and local economic conditions. Each agency responsible for dispersing Recovery Act dollars

provided explicit criteria by which funds would be allocated. For a substantial fraction of these

grants the criteria were unrelated to local economic conditions. For example, the criteria for

the dispersion of money from the Department of Education to children with disabilities across

localities was the relative population of these children, not whether the communities suffered a

recession. Hence, in our analysis we can consider exogenous variations in government spending

by only including money allocated to localities based on criteria unrelated to the business cycle.

A second challenge is to translate our regional findings into a national context. There are

may reasons why a multiplier based on regional variation (relative multiplier) will not coincide

with the aggregate multiplier (Nakamura and Steinsson, 2014). For example, if the regions

receiving government aid are not paying for it then the relative multiplier will be larger than

the aggregate. A similar problem occurs with any type of spillovers across regions due to

government spending.

To translate our empirical regional multiplier into an aggregate multiplier we build a

New Keynesian multi-regional model with spillovers and incomplete markets. In each region

there are heterogeneous households who face idiosyncratic labor income shocks. Markets are

incomplete and households face borrowing constraints. Each region is also populated by a

2

final good firm and a continuum of intermediate good firms. The final good firm does not

use solely local intermediate goods but demands inputs from all the regions. This creates

spillovers in the case of a local government spending shock. To capture the differences in

federal tax liabilities we assume permanent differences in average region productivity and a

progressive tax schedule. Our target is to use our model to match the regional differences in

consumption due to local government spending shocks.

Our paper contributes to the literature analyzing the effects of government spending on

consumption. Blanchard and Perotti (2002) characterize the dynamic effect of shocks in

government spending by using a mixed structural VAR/event study approach. They achieve

identification by using institutional information about the tax and transfer systems and the

timing of tax collections. Ramey and Shapiro (1998) estimate the effect of military build-ups

on a variety of macroeconomic variables. Gorodnichenko and Auerbach (2012) use regime

switching SVAR models to estimate how the effect of fiscal policy varies over the business

cycle. They find that the maximum size of the government multiplier is about 0.9. Also

that policies that increase government purchases have a much larger impact in recession. Hall

(2009) reports that the multiplier based on the effect of military spending is around 0.5 for

output and slightly negative for consumption. Our paper departs from the VAR literature by

exploiting regional differences in government spending and consumption during the period of

fiscal stimulus 2009-2013.

On the other hand the literature that does use regional variation has abstracted from

consumption expenditures. Conley and Dupor (2013) study the effects of the ARRA on

employment. Chodorow-Reich, Feiveson, Liscow, and Woolston (2013) analyze the effect of

government aid administered through the Medicaid reimbursement process on states’ em-

ployment. Shoag (2013) uses defined benefit plans as an instrument to analyze the effects

of government spending on income and employment. To our knowledge ours is the first pa-

per to use cross-regional variation as a tool to study the effects of government spending on

consumption.

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Nakamura and Steinsson (2014) estimate the effects of an increase in government spending

on output using variation in regional military procurement associated with aggregate mili-

tary build-ups and draw-downs. Similar to their paper, we employ a New Keynesian model

to translate the relative multiplier into an aggregate multiplier. A key difference is that we

translate this multiplier within a rich model that includes: (i) heterogeneous households facing

idiosyncratic labor income risk, (ii) incomplete markets and borrowing constraints, (iii) perma-

nent differences in average region productivity, and iv) input-output linkages across regions.

Our framework is more suitable to capture the differential response of households/regions’

consumption to a government spending shock.

As mentioned our paper also speaks empirically to the literature analyzing government

spending at the zero lower bound. Hagedorn, Handbury, and Manovskii (2015) analyze the

effects of unemployment benefits as a source of demand stimulus. They use the Nielsen Retail

Store dataset to study whether inflation was larger at regions with higher unemployment

benefits. Our paper takes two important steps beyond their analysis. First, we look directly

at consumption expenditure differences across regions by using multiple sources for nondurable

and durable consumption. Second, we translate these regional differences using a multi-region,

heterogeneous-agents model with incomplete markets and spillovers.

Finally, our paper is related to Parker, Souleles, Johnson, and McClelland (2013) who

exploit the 2008 transfers that were given to households. The authors use the consumption

expenditure survey and a random difference in the arrival of transfers to compare the change

in consumption for transfer recipients compared to future or past recipients (Kaplan and

Violante, 2014). As the authors acknowledge their estimates capture the partial effect of

government spending on household consumption. In contrast, we look across a larger time

interval to capture the aggregate effects of consumption response. Moreover, our paper uses

a richer set of consumption datasets combining a household-level dataset (Nielsen) with a

macro-level data (state-level BEA).

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2 Data

This project combines multiple datasets. Data on government spending come from the

American Reinvestment and Reenactment Act as found at the www.recovery.org site. Data

on consumption expenditures come from two separate datasets. The Nielsen HomeScan and

Retail Store dataset, and state-level data on consumption expenditures from the Bureau of

Economic Analysis (BEA).

2.1 Government Spending- ARRA

The American Recovery and Reinvestment Act of 2009 (Public Law 111-5) was enacted on

February 17, 2009. The Act is commonly known as the “stimulus package”. The immediate

goals where to spur economic activity and create new jobs. The main were tax cuts and

benefits, unemployment benefits and funding for federal contracts.

To promote transparency the Act required recipients of ARRA funds to report how they

used the money. All the data are posted on Recovery.gov so the public can track the Recovery

funds. In particular, entities receiving ARRA awards (recipients) were required to report

quarterly on the status of the award. May 1 2014 was the last time the website was updated.

For every award one can find information on the total amount awarded, the award date, the

funding agency, and the project location (city, state and zip code).

Among agencies that received awards was the Federal Highway Administration (receiving

10.4% of total grants), the Department of Energy (receiving 8.1% of total grants), the Depart-

ment of Housing and Urban Development (receiving 2.3% of total grants), the Administration

for Children and Families (receiving 1.2% of total grants), and the Department of Educa-

tion (receiving 0.6% of total grants). The money were allocated to several projects such as

developing programs for data analysis of student outcomes, development and modernization

of public housing, affordable housing, development and maintenance of highways and road

rehabilitation, Head Start and other. A large fraction of the federal dollars were channeled

through state and local governments. The Act specified dollar amounts allocated for vari-

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Figure 1: Government spending by U.S. counties

Million $0(0-10](10-20](20-50](50-100](100-500]>500

Note: The Figure shows the cumulative amount of government spending in million dollars during the period 2009-2013 by U.S.

counties.

ous categories; however, local and state governments had much latitude regarding when and

on what projects ARRA dollars were spent. Figure 1 shows the geographical variation in

cumulative spending across U.S. counties during the period 2009-2013.

2.1.1 Instrumental Variable

It is possible that the money allocated to local communities was correlated to local busi-

ness cycle conditions. To deal with this endogeneity we construct an instrumental variable.

In particular, our data offer the opportunity to uncover exogenous movements in government

spending. Each Agency responsible for dispersing Recovery Act dollars provided explicit cri-

6

teria by which funds would be allocated. Hence, we only include money allocated to localities

based on criteria unrelated to local economic conditions.

An example is money given from the Department of Education to children with disabilities.

The criteria for the dispersion of these money across localities was purely the relative popu-

lation of children with disabilities, not whether these localities suffered a recession. Another

example is money provided through the Federal Transit Administration for road improvement

and maintenance. The criteria were the population density and passenger miles of the areas

these roads were located. Overall, we find that nearly 22% of total awards were allocated

based on criteria unrelated to local business economic conditions.

2.2 Consumption Expenditure Data

The construction of local measures of consumption expenditures is the key novelty of our

paper. The most commonly used dataset for consumption expenditures–the Consumption Ex-

penditure Survey—provides information at a relative aggregated level (U.S. States). Moreover,

there are well known issues with measurement errors (Attanasio, Hurst, and Pistaferri, 2013).

For that reason we use information from two separate datasets. The first is the Nielsen Home-

scan Consumer Panel and Retail Stores Data which provides information on consumer retail

purchases. This is a micro-level dataset providing information on household characteristics

including zip code residence. The second data is state-level consumption expenditures from

the Bureau of Economic Analysis. Overall, our paper combines different sources of regional

consumption to provide a comprehensive picture of regional variation in consumption.

Table 1 describes the different data sources used for the analysis. For each source we de-

scribe whether household information is available, the aggregation level, the type of consump-

tion available in the data and the corresponding category. Each data source has something

new to offer for our analysis. The Nielsen data is a panel data that includes household-level

characteristics. It includes information mostly on nondurables (retail purchases). BEA is the

most comprehensive in terms of consumption categories. It includes the total consumption

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Table 1: Data Sources for Consumption Expenditures

Data Source Household-Level Panel Aggregation Consumption Type Category

Nielsen Homescan Yes Yes Zip/County/State Retail Purchases NondurablesNielsen Retail Stores No No Zip/County/State Retail Purchases NondurablesBEA No No State All All

Note: Table describes the different data sources used for the analysis. For each source we describe whether household information

is available, the aggregation level, the type of consumption available in the data and the corresponding category.

expenditures by year in all categories: nondurables, durables, and services. The drawback is

that it is an aggregated data at the state-level.

2.2.1 Nielsen HomeScan

We get data on household-level consumption from Nielsen Homescan Consumer Panel

Dataset. The Consumer Panel Data represents a longitudinal panel of 40,000-60,000 U.S.

households who continually provide information about their purchases.1 The purchases are

recorded by the panelists using in-home scanners.

The data is available from 2004-2012. Demographic variables include household size, in-

come, age, presence and age of children, employment, education, marital status, occupation,

type of residence, and race. Panelists update annually their demographic information. Geo-

graphic information is also available such as the household zip code, county and state.2

The dataset includes detailed information on all households’ shopping trips. In particular,

the dataset records the date of the trip, the UPC code and the total number of units purchased,

and the total amount spent. Using the Nielsen dataset we can link the price charged for every

product by a particular store. Purchases in the Nielsen Home Scan include a combination of

non-durable and durable goods. However, even the durable goods are fast-moving products

1Panelists are randomly recruited via mail or the Internet. Nielsen has ongoing communication withpanelists to ensure cooperation, create enthusiasm and monitor workload. Nielsen has also a number ofsystems to ensure quality data.

2The panel composition is designed to be projectable to the total U.S. population. Since some householdsare more likely to be selected according to their characteristics Nielsen provides sample weights to correct forsample bias.

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Table 2: Fraction of Spending by Store Type–Nielsen HomeScan

Store Type Spending

Grocery 32.9% Convenience store 1.5%Discount store 20.5% Electronics store 1.1%Warehouse club 8.5% Gas mini mart 1.0%Drug store 4.2% Pet store 0.8%Department store 3.9% Restaurant 0.7%Online Shopping 3.0% Office supplies store 0.7%Hardware/Home Improv. 2.9% Quick serve restaurants 0.6%Dollar Store 1.7% Liquor store 0.6%Apparel Stores 1.6% Home furnishings 0.5%

Note: The Table reports the fraction of total spending in all Nielsen categories by Store type. Store types follow the classification

used by Nielsen.

and typically not very expensive. Examples of fast-moving durable goods available in Nielsen

are cameras and office supplies. Table 2.2.1 reports the fraction of spending for each type

of store in the Nielsen dataset. Around 53% of annual spending takes place in Grocery and

Discount Stores. Hardware, Home Improvement, and Electronics Stores account for just 4%

of annual spending. Nielsen also has information on Online Shopping which accounts of 3%

of the annual retail spending in the dataset.

2.2.2 Nielsen Retail Data

Apart from the household scanner data, Nielsen makes available scanner data directly

from retail stores. This dataset consists of weekly pricing, volume, and store environment

information generated by point-of-sale systems from more than 90 retail chains in the U.S.

The years available are 2006 to 2011. For each store there is available information on the store

chain code, channel type and area location. For each UPC code, stores report units and price

sold among others. This allows to measure in an accurate manner the retail expenditures of

every store in a particular area and point in time. Scanner data are available for more than

35,000 grocery, drug, mass merchandiser, and other stores and cover the entire U.S. These

participants cover more than half the total sales volume of US grocery and drug stores and

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more than 30 percent of all US mass merchandiser sales volume. Although our current version

analyzes only the consumer panel, we intend to include the retail data to get an additional

estimate of consumption expenditures in a particular location.

2.2.3 BEA

In December 2015, the U.S. Bureau of Economic Analysis released its first set of official

statistics on personal consumption expenditures (PCE) by state. PCE by state statistics are

released for 16 expenditure categories; eight categories of durable and nondurable goods and

seven categories of services. Nondurable goods are divided into food and beverages, clothing,

gasoline and other. Durable goods are divided into motor vehicles, furnishing and durable

household equipment, and recreational goods. Services include among others, health services,

transportation services, and financial services.

3 Empirical Analysis

3.1 Measurement Framework

To estimate the effect of government spending on consumption we use the following rela-

tionship using household-level consumption data from years 2009-2013

Ci,j,t = a+ β Gj,t +6∑

κ=1

γκ Cons.κi,j,2009 ×Gj,t +Xi,j,t Φ′ + i+Dt + εi,j,t (1)

where Ci,j,t is the consumption of household i in region j in year t. Gj,t is the government

spending in region j in year t. Xi,j,t is a vector of household-specific controls which includes the

number of adults, teenagers, and children under 12 years old in the household, the age of the

head of the household, dummies for the highest educational level of the head of the household,

dummies for the employment status of the head of the household, dummies for the number

of employed members in the household, and finally, dummy for the total household income

10

in year t − 2.3 The household income data are available in six intervals: (1) under $25,000,

(2) $25,000-$35,000, (3) $35,000-$50,000 (4) $50,000-$70,000 (5) $70,000-$100,000, and (6)

$100,000 and above. We interact government spending of Gj,t with household consumption

at base year 2009: Ci,j,2009. We divide households by 6 consumption (1) less than the 10th

consumption percentile (2) between the 10th and 25th percentile (3) between the 25th and 50th

percentile (4) between the 50th and 75th percentile (5) between the 75th and 90th percentile ,

and (6) above the 90th percentile. We estimate Equation (1) using OLS. Coefficient β gives

the increase in consumption expenditures due to a 1$ increase in government spending.

In addition we consider a specification that controls for region-fixed effects.

Ci,j,t = a+ β Gj,t +6∑

κ=1

γκ Cons.κi,j,2009 ×Gj,t +Xi,j,t Φ′ +Dj +Dt + εi,j,t (2)

Equation (1) controls for time- and region-specific fixed effects. In this case the household

fixed effect cannot be separately identified. The year-fixed effects capture aggregate trends

in consumption and the region-specific fixed effects capture region-specific level of consump-

tion. Consequently, the coefficient in government spending captures variation in household

consumption due to variation in the level of government spending received by the area beyond

the region-specific consumption patterns or aggregate consumption patterns in the specific

year. Dj is the region j fixed effect, Dt is year t fixed effect. We estimate Equation (2) using

OLS, clustering standard errors by household’s region j.

It is reasonable to assume that government spending can affect income and thus consump-

tion with some lag. Or that some of the spending in some areas might be anticipated and

thus affected consumption in previous periods. For this reason we expand our specifications

to include the cumulative changes over the period 2009-2013. In particular, we regress the

cumulative change in consumption between years 2009-2013 for household i in region j ∆Ci,j

to the cumulative change in government spending in region i during the same period ∆Gj.

These are given by

3The period that the income refers to is dictated by data availability- a two year lag. This can be changedto t once the data for 2015 become available.

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Figure 2: Cumulative change in consumption over 2009-2013 relative to 2009

2009 2010

∆C2010

2011

∆C2011

2012

∆C2012

2013

∆C2013

Note: The Figure displays a hypothetical impulse response function for consumption. This is the cumulative change in consump-tion expenditures over 2009-2013 relative to the base year 2013.

∆Ci,j =2013∑t=2009

{Ci,t,j − Ci,2008,j} (3)

∆Gj =2013∑t=2009

{Gt,j −G2009,j} (4)

These definition correspond to the impulse response functions using 2009 as a base year.4

Figure 2 gives a graphical representation of Equation (3). Notice that this approach will

pick up any lead/lag effects between governmnet spending and consumption expenditures. To

estimate the effect of government spending on consumption we use the following relationship

∆Ci,j = a+ β ∆Gj +Xi,j,2009 Φ′ + εi,j,2009 (5)

where ∆Ci,j is the cumulative change in consumption of household i in region j over periods

2009-2013. ∆Gj is the cumulative change in government spending in region j over the same

period. We include the same set of control variables as Equations (1) and (2) but for the

base year 2009. Equation (5) is a cross-sectional regression. Coefficient β gives the increase in

consumption expenditures over a 4-year period due to a 1$ increase in government spending

4We assume that Gj,2009 = 0.

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over the same time interval.

Finally we consider a specification that normalizes both the dependent variable and the

regressor by consumption at the base year.

∆Ci,jCj,2009

= a+ β∆Gj

Cj,2009

+Xi,j,2009 Φ′ + εi,j,2009 (6)

Coefficient β gives the percentage increase in consumption expenditures over a 4-year

period due to a 1% increase in government spending over the same time interval.

Data from the BEA are aggregated at the state-level. In that case we cannot use indi-

vidual or regional fixed effects but only cross-regional variation. Hence, Equation (1) and

Equation (2) will become

Cj,t = a+ β Gj,t +Xj,t Φ′ + εj,t (7)

Xj,t represents area specific control variables. We include per capita Adjusted Gross Income

which we obtain from IRS website. As before we construct 6 income groups: (1) less than the

10th income percentile (2) between the 10th and 25th percentile (3) between the 25th and 50th

percentile (4) between the 50th and 75th percentile (5) between the 75th and 90th percentile ,

and (6) above the 90th percentile. Equation (5) and Equation (6) remain the same with the

exception that we use only area-level control variables. We write them down for completeness

∆Cj = a+ β ∆Gj +Xj,2009 Φ′ + εj,2009 (8)

∆CjCj,2009

= a+ β∆Gj

Cj,2009

+Xj,2009 Φ′ + εj,2009 (9)

3.2 Empirical Results

We describe the estimates of our specifications. Table 3 provides the consumption multipli-

er as estimated using Nielsen HomeScan data for specifications with household and area fixed

effects (Equations (1) and (2), respectively) and with the cumulative consumption change

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(Equations (5) and (6)). For all specifications we report estimates with and without controls.

For convenience we do not report here the interaction terms.

All estimates are reported for several levels of aggregation: zip code, county, and state.

This distinction is useful as government spending at an area might spillover and affect nearby

regions. By considering higher level of aggregations we make sure to capture these spillovers.5

Our estimates point to several findings. A regression of Ci,j,t to Gj,t (Equations (1) and

(2)) delivers very small effects. This is true for all level of aggregations. Estimates range

between $-0.005 to $0.037. However, none of these effects are significant. Household controls

do not seem to affect much these small effects. However, a regression of ∆Ci,j to ∆Gj (Equa-

tions (5) and (6)) delivers significant and in some cases quite large coefficients. In particular,

a $1 of government spending in a county increases household consumption expenditure by

around $0.04 in that county, while a $1 of government spending in a state increases household

consumption expenditure by around $0.14-$0.20 in that state. Our analysis confirms that

at higher level of aggregation government spending has larger effects. For example, at the

zip code level the coefficients remain small and insignificant. Equation (6) which should be

interpreted in percentage terms, also delivers large and positive results. When we include

household control variables, a 1% increase in government spending increases consumption

by 0.02%, 0.36% and 1.31%, at the zip-, county-, and state-level, respectively. Overall, the

cumulative regressions point to a positive and significant effect of government spending on

consumption.

Table 4 provides the consumption multiplier as estimated using state-level BEA data.

We report separately the specification using time t consumption and government spending

(Equation (7)) and the specifications with the cumulative consumption change (Equations (8)

and (9)). Again, we report estimates with and without controls which as mentioned is the per

capita adjusted gross income of a state.

We report our estimates separately for each consumption category: non-durable consump-

5Of course they could be spillovers between states which we cannot capture. For this reason we willconsider a multi-regional model with across region spillovers.

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Table 3: Empirical Results—Nielsen HomeScan

Coefficient β Specification

Aggregation Equation (1) Equation (2) Equation (5) Equation (6)

Zip Code -0.003 0.004 -0.005 -0.001 0.009 0.002 0.021∗∗∗ 0.027∗∗∗

(0.003) (0.003) (0.003) (0.002) (0.006) (0.007) (0.006) (0.007)

County 0.005 0.001 0.008 0.013 0.042∗∗ 0.047∗∗ 0.353∗∗∗ 0.360∗∗∗

(0.019) (0.016) (0.022) (0.018) (0.013) (0.022) (0.027) (0.027)

State 0.037 -0.010 0.019 -0.001 0.143∗∗ 0.201∗∗ 1.280∗∗∗ 1.313∗∗∗

(0.117) (0.106) (0.111) (0.106) (0.081) (0.079) (0.054) (0.057)

Control Variables No Yes No Yes No Yes No Yes

Interaction Terms No No No No No No No No

Note: The Table gives the empirical estimates using Nielsen HomeScan dataset. Standard errors are given in parenthesis. One,two, and three stars correspond to significance at the 10%, 5%, and 1%, respectively. We adjust consumption by the householdsize and trim the distribution at the 5% and 95%.

Table 4: Empirical Results—BEA

Coefficient β Specification

Consumption Group Equation (7) Equation (8) Equation (9)

Non-Durables 0.713∗∗∗ 1.793∗∗∗ 0.290∗∗∗ 0.323∗∗∗ 0.225∗∗ 0.293∗∗

(0.173) (0.322) (0.092) (0.101) (0.106) (0.114)

Durables 0.304∗∗∗ 0.651∗∗∗ -0.029 -0.083 -0.021 -0.023(0.115) (0.185) (0.062) (0.065) (0.068) (0.073)

Services 1.502 6.144∗∗∗ 1.706∗ 1.854∗∗ 2.095∗∗∗ 1.894∗∗∗

(2.776) (1.809) (0.876) (0.869) (0.663) (0.668)

PCE 4.986 11.310∗∗∗ 2.588∗∗ 2.803∗∗ 2.268∗∗ 1.875∗∗

(3.357) (2.319) (1.219) (1.200) (0.846) (0.837)

Control Variables No Yes No Yes No Yes

Interaction Terms No No No No No No

Note: The Table gives the empirical estimates using state-level data from the BEA. Standard errors are given in parenthesis.One, two, and three stars correspond to significance at the 10%, 5%, and 1%, respectively.

tion, durable consumption, services, and total personal consumption expenditures. Estimates

from Equation (7) point toward strong effects of government spending on all consumption

categories. If we do not control for income, a $1 of government spending increases the per

capita state’s nondurable consumption expenditure by around $0.71. Durable consumption

expenditures increase by around $0.30 while services by $1.50 although this is not significant.

15

If we include controls these estimates become larger and more tightly estimated.

When we consider estimates from our cumulative specifications (Equations (8) and (9)) the

effects become smaller but in most cases still significant. Surprisingly, the coefficient for non-

durable consumption of around $0.3 is in line with the state-level coefficient we found from the

Nielsen dataset. In this specification the coefficient for durable consumption becomes slightly

negative but is not significant. The multiplier for expenditure on services remains large and

somewhat significant which drives an also large total consumption multiplier.

4 Relative vs. Aggregate Multiplier

Our empirical estimates point toward a significantly positive consumption multiplier es-

pecially for nondurables. However, translating these regional findings into a national context

might be problematic. For example, if the regions receiving government aid are not paying

for it then our estimates will be overestimating the aggregate effect. A similar problem occurs

with any type of spillovers across regions due to government spending. Regional estimates

can also mask effects taking place through changes in the real interest rate. In this section we

attempt to illustrate these issues through some graphical examples.

The left panel of Figure 3 analyzes the case of positive spillovers. In this example, region

A receives 0$ of government aid and region B 1$ of aid. For region A the cumulative change

in consumption ∆CA over a time period is 0.3$. This can be attributed to a common trend

affecting consumption absent of government aid (e.g. business cycle). For region B the

cumulative change in consumption ∆CB over a time period is 0.4$. This is due to the common

trend and the government aid of 1$. Hence, based on this analysis one would conclude that

1$ in government aid can increase consumption by 0.1$ i.e the multiplier is 0.10.

If there are no spillovers between regions A and B we could conclude that 1$ in governmnet

spending affects national consumption by 0.1$. But assume that region A also benefits from

the 1$ in region B. For example, some consumers in region B may purchase their products

from region A increasing income and consumption in region A by 0.1$ as well. Since region B

16

Figure 3: Relative and Aggregate Multiplier

A. Spillover effects∆C

∆G1$

0.5$

0.4$

0$

0.2$

0.3$

Aggregate ∆C

Relative ∆C

B. General equilibrium effects∆C

∆G1$0$

0.3$

0.4$

Aggregate ∆C

Relative ∆C

increased consumption by 0.1$ relative to Region A the total increase in region B’s consump-

tion is 0.2$. And the aggregate multiplier is 0.3$ much larger than the relative multiplier of

0.1$. Taxes can be an example of negative spillovers if county A bears a higher burden in

taxes to subsidize the government aid in county B. In that case we overestimate the multiplier.

A similar problem arises if the government spending of 1$ affects both regions A,B through

some change in the interest rate. The right panel of Figure 3 analyzes this case. As before,

region A receives 0$ of government aid and region B 1$ of aid which leads to a relative

multiplier of 0.10. However, government spending may increase the real interest rate which

will affect both regions. For example, the real interest rate increase may decrease consumption

in both regions by 0.1$. This means that in absence of government aid the national change

in consumption would be 0.4$ not 0.3$ computed based on our regional analysis. Since 1$ in

government aid decreases consumption in both regions by 0.1$ and since region B increased

consumption relative to region A by 0.1$, the national multiplier will be -0.1$ not 0.1$ found

before.

To address these identification issues we build a model that incorporates spillovers, differ-

ential taxation across regions and general equilibrium effects.

17

5 Model

5.1 Demographics

The economy is divided in i = {1, .., N} regions. Each region is populated by a measure

one continuum of households and produces a final good Yi using intermediate inputs produced

by monopolistically competitive firms. In each region there is a continuum of intermediate

good firms. Each firm is indexed by j. The intermediate good firm j located in region i

produces yi,j.

5.2 Households

Each region is populated by a measure one continuum of households. Households derive

utility from consumption and leisure. A household is endowed with one unit of productive

time, which it splits between work h and leisure. Households’ decisions depend on preferences

representable by a time separable utility function of the form

U = E0

[∞∑t=0

βt−1

{C1−σi,t

1− σ+ ψ

(1− hi,t)1−θ

1− θ

}](10)

where β is the discount factor and θ affects the Frisch elasticity of labor supply. Ci is a

composite good defined as

Ci =

[N∑i=1

α1φ

i,i′ cφ−1φ

i,i′

] 1−φφ

(11)

ci,i′ is the consumption of good i′ by region i. αi,i′ represents the preference toward the

final good of region i′ by region i. Households supply labor h in the intermediate good sector

and receive (real) wage payments wi. Moreover, each household draws an idiosyncratic shock

that follows an AR(1) process in logs:

log z′ = ρ log z + η′, with η′ ∼ iid N(0, σ2η). (12)

18

The transition matrix, which describes the autoregressive process, is given by Γxx′ . Total

labor earnings zwh are taxed using the tax function T (.). Profits from the intermediate good

sector sector are uniformly distributed to households in the region. Each household receives

a dividend D. Households use a one-period bond b to insure against adverse productivity

shocks. In nominal terms the bond costs costs 1 unit and pays (1 + i) where i is the nominal

interest rate. Households are not allowed to borrow. The government will supply the asset.

We write the household’s problem in a recursive way. The state variables are the house-

hold’s real bond holdings b, the stochastic productivity z and an vector S summarizing the

aggregate prices and quantities. The value function is:

Vi(z, b,S) = maxc,b′,h

{C1−σi

1− σ+ ψ

(1− hi)1−θ

1− θ+ β

∑z′

Γz,z′Vi(z′, b′,S′)

}(13)

s.t. Ci + (1 + πi,t+1)b′i = zwhi − TL(zwhi) + (1 + it)b+Di (14)

πi,t+1 is the region-specific inflation rate defined as

πi,t+1 =Pi,t+1

Pi,t− 1 (15)

where Pi is the price aggregator in region i (defined below). We can derive the demand

equation final good i by households in region i′ ci,i′

ci,i′ = αi,i′P−φi′

P−φiCi (16)

Pi′ is the price of final good produced in region i′. The price aggregator in region i is

Pi =

[N∑i′=1

αi,i′ P1−φ

i′

] 11−φ

(17)

The aggregate state vector will be defined later.

19

5.3 Firms

Final good firms In each region there is a final good firm producing Yi using intermediate

inputs. Final good firms do not use only locally produced intermediate inputs but from all

regions in the economy. The demand by final good firm i for an input produced by firm j

located at region i′ is xi,i′,j. The technology of the final good firm in region i is

Yi =

[N∑i′=1

γ1ε

i,i′

∫j

xε−1ε

i,i′,j

] 1−εε

(18)

The parameter ε captures the substitutability between intermediate goods within a region.

The parameter γi,i′ captures the preference of final good firm i for intermediate inputs from

region i′. These parameters will capture spillovers across regions. The final good firms make

zero profits. The price charged by each final good firm will depend on the intermediate input

prices. Let pi,j be the price of intermediate good j in region i. Then we can define the final

good price in region i as the price aggregator:

Pi =

[N∑i′=1

γi,i′

∫j

p1−εi′,j

] 11−ε

(19)

Intermediate good firms Each region i has a continuum of intermediate goods indexed

by j. The intermediate good yi,j is produced using only labor. We assume that labor cannot

move across regions. Firms use a linear technology

yi,j = Li (20)

where Li is the labor supplied by region i households. Firms sell their product to final

good firms at price pi,j. The intermediate good firm faces demand from all N final good firms.

Firm j located in region i′ faces demand by final good firm i equal to xi,i′,j. In particular, this

will be given by

20

xi,i′,j = γi,i′p−εi′,jP−εi

Yi (21)

The aggregate demand for region i intermediate good firm j will be

yi,j =N∑i′=1

xi′,i,j (22)

Due to monopolistic competition, the intermediate good firm will take the demand into

account when setting its price pi,j. We assume that prices are sticky. For each firm there

is a probability (1 − λ) to change its price next period. We assume that in every region

the intermediate good firms are controlled by a risk-neutral manager who distributes to local

households all profits immediately. The real value of firm j in region i is given by

maxpi,j

∞∑s=0

(λβ)s{pi,j,t+sPi,t+s

yi,j,t+s − wi,t+sLi,t+s}

(23)

This leads to the optimal pricing equation

p∗i,j,tPi,t

=ε

ε− 1

Γt∆t

(24)

Γt = wi,tyi,j,t + λβ(1 + πt+1)1+εΓt+1 (25)

∆t = yi,j,t + λβ(1 + πt+1)ε∆t+1 (26)

Let p∗i,j,t is the reset price by firm j in region i. Using Equation 19 we can derive the

inflation rate for region i.

Pi =

[N∑i′=1

γi,i′ [λp∗i′,j,t1−ε + (1− λ)P 1−ε

i′,t−1]

] 11−ε

(27)

If regions where homogeneous Pi = Pi′ the above equation would turn into the more

familiar expression

21

(1 + πi,t) =

1− λ

1− λ∑N

i′=1

p∗i′,j,tPi,t

1−ε

1

1−ε

(28)

Total profits distributed to households in regions i are Di =∫jdi,j where di,j equal to

di,j = pi,jyi,j − wiLi,j (29)

Finally combining Equation (20) and Equation (21) we derive

′∑i

∫j

xi,i′,j = Yi[λp∗i,j,tPi,t

−ε

+ (1− λ)(1 + πi,t)ε] (30)

5.4 Government

A federal government spends a total amount G every period. G is the sum of spending in

every region i

Gt =N∑i=1

Gi,t (31)

The fiscal authority finances this spending using progressive labor income taxes. Total

taxes from all regions are

Tt =N∑i=1

∫µ

T (zwi,thi,t) (32)

The government can also finance its spending by issuing a government bond. The bond is

in fixed supply B̄. Hence, the government budget constraint reads

B̄ + Tt = Gt + (1 + it)Bt (33)

22

5.5 Monetary Authority

We consider a simple monetary policy where the central bank sets the nominal interest

rate based on a Taylor rule

it = max[0, iss + φπat ] (34)

where πat =∑N

i=1 πi,t is the inflation rate in the economy.

5.6 Aggregate State Vector and Equilibrium

The aggregate state vector contains the distribution of households over bonds and pro-

ductivity µ(b, z) as well as the decision of intermediate good firms over production and prices

{yi,j, pi,j}Ni=1 ∀j.

Given an exogenous distribution of government spending {Gi}Ni=1 over regions, a symmetric

stationary equilibrium consists of a sequence of regional prices {wi,t, πi,t, pi,j,t, Pi,t}Ni=1 ∀j, t an

interest rate i, firm quantities {yi,j, xi′,i,j, Yi}Ni=1∀j, t, policy and value functions {b′i, hi, Vi(z, b,S)}Ni=1

s.t.

1. Bond market clears∑

i

∫µb′i = B̄

2. Labor market clears∑

i

∫µhi =

∑i

∫jLi,j

3. Goods market clears Yi = Ci +Gi ∀i

4. Reset pricing satisfies Equation (24) ∀i

5. Regional price Pi follows Equation (27) ∀i

6. Production function follows Equation (30) ∀i

7. Dividends are given by Di = Yi − wiLi ∀i

8. Government budget clears B̄ + Tt = Gt + (1 + it)Bt

23

9. Interest rate is set based on Taylor rule it = max[0, iss + φπat ]

6 Quantitative Analysis

To be completed

7 Conclusion

The empirical VAR literature has no consensus on the whether government spending re-

duces of enhances private consumption spending. More importantly, standard VAR/event

techniques are not informative of the consumption multiplier during periods of zero nominal

interest rates. We set up a novel exercise to tease out the effect of government spending

on consumption when the economy is at the zero lower bound. In particular, we construct

local measures of consumption expenditures and exploit the regional variation in government

spending during the period 2009-2013.

We find significantly positive effects of government spending on consumption at all levels of

aggregation. For example, at the state-level, nondurable consumption expenditures increased

by around $0.25 for every additional dollar in government aid. To translate our regional find-

ings into an aggregate context we build a New Keynesian multi-regional model with spillovers

and incomplete markets. Our target is to use our model to match the regional differences in

consumption due to local government spending shocks.

24

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