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WORKING PAPER
ALFRED P. SLOAN SCHOOL OF MANAGEMENT



A Tax-Based Test for Nominal Rigidities

by

James M. Poterba, Julio J. Rotemberg and
Lawrence H. Summers



SSM WP#1657-85



April 1985



MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

CAMBRIDGE, MASSACHUSETTS 02139



A Tax-Based Test for Nominal Rigidities

by

James M. Poterba, Julio J. Rotemberg and
Lawrence H. Summers



SSM WP#1657-85 April 1985



A Tax-Based Test for Nominal Rigidities.



James M. Poterba
MIT and' NBER



Julio J. Rotemberg
MIT and NBER



Lawrence H. Summers
Harvard University and NBER



April 1985



We are indebted to Craig Alexander and Ignacio Mas for outstanding research
assistance, to Olivier Blanchard, Rudiger Dornbusch, Stanley Fischer, and
Greg Mankiw for helpful discussions , and to the National Science Foundation
for financial support. Frank DeLeeuw of the U.S. Bureau of Economic
Analysis, and R. Doggett, K. Newman, and A. Tansley of the U.K. Central
Statistical Office, provided us with unpublished data. This research is part
of the NBER programs in Taxation and Economic Fluctuations. Views presented
do not necessarily reflect those of the NBER or NSF.



SEP 2 4 1985
RECEIVED



April 1 985



A Tax-Based Test for Nominal Rigidities

ABSTRACT

In classical macroeconoraic models with flexible wages and prices,
whether a tax is levied on producers or consumers does not affect its
incidence. However, if wages or prices are rigid in the short run, as they
are in Keynesian macroeconomic models , then shifting a tax from one side of
the market to the other may have real effects. Tax changes therefore provide
potential tests for the presence of nominal rigidities. This paper examines
the price and output effects of revenue-neutral shifts between direct and
indirect taxation. The results, based on post-war data from both Great
Britain and the United States, reject the view that wages and prices are
completely flexible in the short run.



James M. Poterba

Department of Economics

M.I.T.

Cambridge, MA 02139

(617) 253-6673



Julio J. Rotemberg

Alfred P. Sloan

School of Management

M.I.T.

Cambridge, MA 02139

(617) 253-2956



lawrence H. Summers
Department of Economics
Harvard University

Cambrdige, MA 02138
(617) 495-2447



The side of a market on which a tax is levied is irrelevant in the
standard nicro economic analjrsis of taxation. Students in- elementary
economics learn that it makes no difference whether a sales tax is collected
from buyers or sellers. They are taught that the ultimate incidence of a
payroll tax depends on the elasticities of supply and demand for labor, not
on whether the tax is levied on employees or employers. Broader equivalence
results concerning sales and income taxes are at the heart of the analysis of
general equilibrium tax incidence. Standard Keynesian macroeconomic analyses
take a very different view. Raising sales taxes is thought to be
inflationary, even if monetary policy remains unchanged. There is leas
concern that increases in direct taxation will increase the price level.

The microeconomic and Ke3mesian views diverge because the former
presumes that all wages and prices are fully flexible, while the latter
postulates rigid nominal wages. With wage rates fixed in the short run,
sales tax increases necessarily raise prices; raising income taxes has no
such effect. If nominal wages are rigid over reasonable lengths of time,
then the conventional tax analysis must be altered. Holding monetary policy
constant, increases in the price level translate point for point into
reductions in output. Even a temporary one percent decline in GNP could
dwarf the potential efficiency gains from many proposed tax reforms.

The very existence of nominal rigidities is a subject of contemporary
macroeconomic debate. Many Keynesian scholars take it as self-evident that
nominal wages are sticky, at least in the short run. For example, Solow
(1980) invites his readers to "accept thi apparent evidence of one's senses
and take[s] it for granted that the wage does not move flexibly to clear the
labor market." Other researchers claim that there is no available evidence
in support of this hypothesis. For example. King and Plosser (1984) write



that "Keynesian models typically rely on implausible wage or price
rigidities, from the textbook reliance on exogenous values to the recent more
sophisticated effort of Fischer that relies on nominal contracts."

Examining how changes in the money stock affect macroeconomic activity,
a standard test for nominal rigidities, is unlikely to resolve this issue
conclusively. Shifts between direct and indirect taxation can provide tests
which avoid many of the difficulties with money-based tests, since they are
less likely to be endogenous responses to macroeconomic events. This paper
employs both British and American data to investigate how shifts in the
direct versus indirect tax mix affect wages, prices, and output. Our results
support the existence of nominal rigidities and suggest that they may have
important effects which should be recognized when analyzing the short-run
effects of tax reform.

The paper is divided into five sections. Section I clarifies the
equivalence of direct and indirect taxation when wages and prices are fully
flexible. It also shows how these equivalences fail when nominal rigidities
are introduced. Section II describes our methodology for examining the
impact of tax changes. The next section explains how we constructed
effective direct and indirect tax rates for Britain and the United States .
Section TV presents our empirical findings. ¥e examine post-war time series
evidence from both countries, and also report a specific analysis of the 1979
"Thatcher experiment" in Great Britain. Tliis tax change raised indirect
taxes while lowering direct taxes commensurately, providing a strong test for
the presence of nominal rigidities. The concluding section sketches the
implications of our results for the analysis of tax policy and macroeconomic
fluctuations.



I. Shifts From Direct to Indirect Taxation: Classical and KeynesiaTi Views

In textbook public finance models, the legal incidence of a sales tax
is of no consequence. It does not matter whether the tax is collected from
producers or consumers. The important variables are the net price which
producers receive and the gross price which consumers pay. Suppose producers
of a good receive P dollars per unit sold and consumers pay P(l+Q) dollars
per unit they buy. Whether producers receive P(1+Q) dollars and hand over P6
dollars to the government or the PG dollars are collected from the consumers
directly has no effect. If the government ceases to collect the tax from
consxmers and starts levying it on firms, firms simply raise their price by
PG. The total amount consumers pay per unit and the net amount received by
firms remains constant.

The absence of short run wage and price flexibility is the essence of
Keynesian models. If the price producers charge consumers is temporarily
fixed, then the legal incidence of a sales tax does matter. A switch from
collecting PG dollars from consumers to collecting them from producers
reduces the price paid by consumers to P, while the price received by firms
falls to P(1-G). This change affects real decisions.

This example of a sales tax in one market is only illustrative. More
generally, switches between income taxes and value added or sales taxes,
which essentially change the side of the market on which the tax is levied,
have real consequences when there are rigidities of the standard Keynesian
sort. "Hie equivalence theorems of Break (1974) and McLure (1975) establish
that in an economy without savings and with flexible prices , a sales tax on



■'■ . See for example Musgrave and Musgrave (1977, Chapter 20).



all goods is equivalent to an equal- revenue tax on all income.'^ This section
begins by presenting a stylized classical macroeconomic model in which these
results obtain. The second half of the section introduces wage and price
stickiness and demonstrates the failure of these familiar incidence results.

I. A. The Classical Framework

The equivalence between sales and income taxation is easily
demonstrated in a simple classical macroeconomic model with perfectly
flexible wages and prices. In the short run, aggregate output (Y) is a
function only of labor input (L):

Y = f(L). (1)

With competitive firms, a notional aggregate labor demand schedule can be
obtained by equating the marginal product of labor to the firm's real wage:

f(L) = w/s (2)

where w is the nominal wage and s is an index of prices received by firms .
Ihe notional supply of labor depends on the purchasing power of the worker's
payment for an hour of work:

L = g[w(l-T)/s(l+G)] (3)

where t is the income tax rate and 9 is the value added tax rate. Labor
supply is unaf:^ected by any reform which does not change (1-t)/(1+G).



^. The equivalence of a sales tax on all goods and a value added tax has
been recognized by many authors. For a particularly clear discussion see
McLure (1984).



Ihe government raises revenue from both income and sales taxes. Tax
collections, T, are defined by

T = Tl + 0(E+G) (4)

where I is pre-tax household income, E is pre-tax household expenditure on
goods and services, and G is pre-tax goveriment spending. Government
spending is treated as exogenous; the national income identity requires that
G = I-E. The household budget constraint in our one period model is

(1-t)I = (U0)E. (5)

To measure the government's effective tax revenue, we focus on tax receipts
collected from the private sector: T* = T - 0G. Using (4) and (5),

T* = I 1: + Q^^-'^) I T

= [1 - (l-r)/(l+0)]l. (6)

Since I depends only on L which depends only on (1-t)/('1+0) , T* depends only
on (1-t)/(1+0). It is therefore independent of changes in the composition of
taxes which leave this ratio "constant.^

We now consider the effects of increasing and reducing t, while
leaving (1-t)/(1+0) constant. Clearly both the real wage paid by firms (w/s)
and the real wage received by workers ( (I -t)w/(1 +0)s J are unaffected, so
output is constant. The price level must change, however. Let a(Y) define
the demand for money balances. Equilibri\im requires that

where M is the nominal money supply. We have followed the standard practice



For small values of 0, the constancy of (1-t)/(1+0) is equivalent to th(
constancy of (t+0).



of assuming that the demand for real money balances, deflated by product
prices, depends on real output. Since output is unaffected by the tax shift,
absent a change in M the after- tax price level, s(l+€i), will not change. An
indirect tax increase will therefore lower s in proportion to the increase in
(1+6). Similarly, since w/s remains constant, the nominal wage must fall.**

Alternative approaches might postulate that money demand depends on
households' disposable income, (1-t)Y, or that money balances should be
deflated by an index of consumer prices. In the former case, a revenue
neutral shift towards indirect taxation would reduce prices , while in the
latter case, it would raise them. In neither case would real output be
affected. Mankiw and Summers (1984) present some evidence suggesting the
empirical relevance of the case where money demand depends on household
expenditure. Regardless of the money demand specification, tax changes will
not affect the price level if nominal output is held constant.

Although shifts between direct and indirect taxes are neutral in this
model, increases in either are not. Combining (2) and (3) it can be seen
that reductions in (1-t)/(1+0), which correspond to tax increases, lower
equilibrium employment and output. This may raise prices. Blinder (1973)
among others argues that prices may also be subject to a countervailing
force, since tax increases may depress aggregate demand and lower
prices. These nonneutralities , even when prices are fully flexible, make it
difficult to interpret previous empirical studies of inflation and indirect



A change in the direct tax rate would also affect the after-tax interest
cost of holding money. However, these effects are likely to be trivial.



taxes ^ as shedding light on the presence of nominal rigidities. These
studies establish only that nominal magnitudes tend to increase when taxes

rise.

The equivalence between direct and indirect taxation on the same tax
base follows from the logic of budget constraints and is not specific to the
simple model considered here. In a multiple- period model, strict equivalence
requires that the sales tax be levied on all goods including new investments.
In an open economy, equivalence requires that sales or value added tax be
collected on imported but not exported goods. This is done in practice as
described by McClure (1983)« Our Appendix demonstrates the equivalence of
direct and indirect taxes in an extremely general context.

I. B. The Keynesian Framework

The hallmark of Keynesian models is that nominal adjustments require
time. Changes in the stock of money or shifts between direct and indirect
taxation, which have no long run real effects, therefore may have important
short run consequences. We illustrate this proposition by considering three
different types of nominal rigidities .

Sticky nominal wages are the primary rigidity in most Keynesian models.
They arise both in textbook Keynesian models and in contracting models such
as that developed by Fischer (1977). Customarily, sticky wages are analyzed



^. Some studies, such as Tait (1980), have investigated the inflationary
effects of introducing value added taxes in European countries. These policy
changes are hard to interpret, however, because in many cases the VAT simply
replaced previous indirect taxes, such as turnover taxes. In other cases,
the imposition of VAT substantially raised the total direct and indirect tax
burden; this could have real effects. Other related work, such as Gordon
(1971), provides some evidence that changing payroll tax rates in the United
States are reflected in the price level. A survey of the broader literature
on indirect taxes and inflation may be found in Nowotny (198O).



bj;- adding a description of wage behavior to the classical model, while
deleting the requirement that notional labor supply equal notional labor
demand. Since both explicit and implicit contracts seem to be denominated in
terms of pre-tax wages, we assume pre-tax wage rigidity. Since post-tax
wages do not need to adjust to tax shifts, rigidities in (1-t)w do not imply
that shifts between direct and indirect taxation have real effects.

Consider an increase in 9 which does not change (1-t)/(1+0). With
sticky wages, w is too high after such a shock. If firms are to remain on
their notional labor demand schedules, employment must fall or prices must
rise. In equilibrium, both occur to some extent since a fall in
employment lowers output and therefore requires an increase in s(l+6) to
satisfy (?)• Keeping w constant, (1), (2) and (?) imply that the
elasticity of the tax inclusive price with respect to a tax change is:



51og(3(l+0))

5log(1+0)



-^'^'^/^^ > 0. (8)

M/(l+0)-a'f'w/f"
w=w



An increase in indirect taxes is like a supply shock , since prices rise and
output falls. Real wages also rise, inducing firms to demand less labor and
produce less output.

A second type of rigidity is real wage resistance, which Branson
and Rotemberg (1980) and Sachs (1979) found in continental European
countries. It can arise from indexing clauses which do not contemplate



This term is usually applied to shocks such as increases in the price of
an imported intermediate input (see Gordon (1975), Blinder (1981), or
Rotemberg (1983'b)). These shocks raise some prices, lowering real money
balances and output if prices are sticky.



tax reforms. If wages are indexed to the consumer price index, 3(1+0),
then increases in will raise w/s . This induces firms to fire
workers, lower output, and raise prices after a revenue neutral shift toward
indirect taxation.

We have examined the effects of two types of wage rigidity. At the cost
of some additional complexity, we could also allow for price rigidity as
urged by Blanchard (1984,1935) and Rotemberg (1982). This would not alter
the basic Keynesian prediction that revenue neutral shifts towards indirect
taxation raise prices and reduce output. Rigidities in s would lead to
increases in s(l+0) when rises. ^ This lowers aggregate demand and induces
firms to fire workers, possibly reducing real wages along the notional labor
supply curve.

We have isolated a clear difference in the empirical implications of
models with and without nominal rigidities. A natural way of testing for the
existence and importance of these rigidities is to examine the response of
prices and output to changes in tax structure, controlling for total revenue
collections. Tliese tests, while not totally free of ambiguity, are superior
to tests of the relationship between money and output for detecting nominal
rigidities. First, tax structure changes are more likely to be exogenous



' » If indexing clauses keep w/s or w(l -t)/s(1 +0) constant, then changes in
unaccompanied by changes in (1-t)/(1+0) will have no real effects. These

variables are not affected by tax reforms even when all prices are
flexible.

^ - With real wage rigidities, an increase in indirect taxation could
trigger a period of inflation. The nature of this inflation is extremely
sensitive to assimptions about the dynamics of wage adjustment; see
Poterba, Rotemberg, and Summers (1985) for further discussion.

. Rigidities in s(l+0) would have no effect in isolation, since s(l+0) does
not change when changes. However, combined with rigid nominal wages,
rigidities in s(l+0) may prevent the tax-inclusive price from rising
immediately and lead instead to a period of inflation.



10



policy shocks than are changes in the money stock. King and Plosser (1984)
argue that changes in the money stock may be endogenous. They establish that
most of the observed correlation between money and output arises from changes
in the money multiplier, not from changes in the stock of base money.
Second, as shown in Grossman and Weiss (1985) and Rotemberg (1984), changes
in the money stock which are engineered through open market operations are
likely to have real effects even without nominal rigidities. Some tax
changes suffer from similar difficulties, because they have incentive and
distributional effects which may change real magnitudes. However, by
considering increases in indirect taxes compensated by reductions in direct
taxes, we minimize these problems.



11



II. Hethodolo'^y

We U3e both British and American data in studying the effects of tax
changes. Britain has experienced considerably more variation in tax
structure than the United States, and it therefore provides better tests for
the presence of nominal rigidities. Our aim is to discover whether, and how,
revenue-neutral chaao*-:?'? i/i t nnd Q affect prices, wages, and output. We test
for nominal rigidities with a minimal set of maintained assumptions by
studying reduced form equations which include a variety of standard aggregate
variables.^ We investigate whether the mix of direct and indirect taxes
improves the explanatory power of these equations. Other variables are
included to prevent tax switches from appearing significant only because they
are correlated with relevant excluded variables.

We estimate two systems of equations. The first consists of three
reduced form equations for the logarithms of prices (p-*.), no;iiinal after-tax
wages (w^(l-T^)), and output (y+). The explanatory variables are lagged
prices, wages, and output, as well as real government deficits (d.) and the
logarithm of the money stock (m.). We also include three tax variables.
The first, TTOT, is the sum of the direct and indirect tax rates. The second
is TMIX, the difference between the direct and indirect tax rates. Including
both TMIX and TTOT is equivalent to including indirect and direct taxes
separately. However, since we are interested primarily in the effect of
switches between direct and indirect taxes holding their sum constant, this
specification is more natural. The third tax variable, OTAX, is the ratio of
tax receipts which we classify as neither direct nor indirect taxes to GNP.



^ . Our reduced form specifications could be derived from a wide class of
structural models.



This gvstem of reduced form equations can be vritten as



,11



- -




?t




w*

u


SZ.


^t




m. *





a (L) a (L) a (L)

p w y

a^pd) cr;(L) a2(L)



a5(L) (r^(L) a^CD
p w y



t-1



t-1



t-1



a' (L^



a"(L)



cr5(L)

m



%.(-)



a;(L;



a^(L)





■-"t




St














+


^2t




OTAX

X




^3t




WIIX^




- -^




- ^







where the a (L)'s are second-order lag polynonials. We found that further
lagged variables had little explanatory power. Each equation in the system
also includes a time trend and seasonal dummy variables.

The equations in (9) include both the money supply and the deficit as
controls for the state of government economic stimulus. These are
essentially predetermined policy variables. In principle, it would also be
desirable to control for shocks to the money demand equation which influence
prices and output. If policy is set so as to offset these shocks, it may be
appropriate to use nominal GNP as a summary variable for the effects of
aggregate demand policies. These considerations led Gordon (1982) to pioneer
the use of nominal GNP in wage and price equations. While this approach
captures velocity shocks, it may capture too much: the disadvantage of
including nominal GNP in these equations is that it may not be a
predetermined variable.



(9)



11



This system of equations can be thought of as emerging from a structural



model like that of ELanchard (1985), which includes an aggregate demand
equation, a pricing equation and a wage setting equation.



1 1



We estimated a second systen of only two equations, for nonmal after-
tax wages and prices, which included current and lagged nominal ST'P in place
of the deficit and tne money supply. ILiis system of equations is given by



fpVD p[.(L?



p2(L) p2(,)





-






pt-1


+




>-1_





P;(L)


... P^(L)




^t




•f


^t


P^(L)


... P^(L)




OTAX^




.'2t.



(10)



where n^ is the logarithm of nominal GNP. In this system, movements in
output for a given nominal GNP can be calculated from price movements.

Systems (9) and (10) allow for unrestricted wage, price, and output
responses to shifts between direct and indirect taxation. Both Keynesian and
classical models imply, however, that revenue neutral tax switches are
neutral in the long run. We therefore impose long-run neutrality, while
testing for short- run TMIX effects, by restricting the sum of the TMIX
coefficients in each equation to equal zero. The short- run tax neutrality
hypothesis implies the restrictions



in system (9) and



V 4^^) = 4^^^ - 4^^^



H-: p^ (L) = p2(L) =
Ox X



=



in system (10). As long as TMIX is a valid exogenous variable, rejection of
Hq is very unfavorable to the classical model. In Section IV we consider
some, in our view unlikely, reasons why TMIX might appear to matter even if
wages and prices were perfectly flexible.



14



After rejecting these null hypotheses, we focus on the relevance of
these rejections for the presence of nominal rigidities. If nominal
rigidities are present, then we expect prices to rise and output to fall for
some time after a tax switch. The response of real wages depends on whether
price or wage rigidities are more important. To investigate these dynamic
effects, we compute our systems' predicted responses to a permanent change in
TMIX. We also followed Mishkin' s (1979) approach and examined the effect of
a TMIX impulse given its actual stochastic process. This procedure avoids
the problems which might arise if permanent shocks to TMIX are widely at
variance with the historical experience. Because the results were very
similar to those for permanent shocks , only the latter are reported in
Section IV.

The reduced forms described above may be subject to some of the
criticisms which have been directed at the vector autoregression approach of
Sims (1980). We have not posited an explicit structural model, and the
parameters in our reduced forms might vary with changes in the policy regime.


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Online LibraryJames M PoterbaA tax-based test for nominal rigidities → online text (page 1 of 4)