Munich Personal RePEc Archive

Should a Government Fiscally Intervene

in a Recession and, If So, How?

Harashima, Taiji

Kanazawa Seiryo University

2 April 2017

Online at https://mpra.ub.uni-muenchen.de/78053/

MPRA Paper No. 78053, posted 31 Mar 2017 09:03 UTC

Should a Government Fiscally Intervene in a Recession and, If So, How?

Taiji HARASHIMA*

April, 2017

Abstract

The validity of discretionary fiscal policy in a recession will differ according to the cause and

mechanism of recession. In this paper, discretionary fiscal policy in a recession caused by a

fundamental shock that changes the steady state downwards is examined. In such a recession,

households need to discontinuously increase consumption to a point on the saddle path to

maintain Pareto efficiency. However, they will not “jump” consumption in this manner and

instead will choose a “Nash equilibrium of a Pareto inefficient path” because they dislike

unsmooth and discontinuous consumption and behave strategically. The paper concludes that

increasing government consumption until demand meets the present level of production and

maintaining this fiscal policy for a long period is the best option. Consequent government debts

can be sustainable even if they become extremely large.

JEL Classification code: E20, E32, E62, H20, H30, H63

Keywords: Discretionary Fiscal policy; Recession; Government consumption; Government

debts; Pareto inefficiency; Time preference

*Correspondence: Taiji HARASHIMA, Kanazawa Seiryo University, 10-1 Goshomachi-Ushi,

Kanazawa-shi, Ishikawa, 920-8620, Japan.

Email: [email protected] or [email protected]

1

1 INTRODUCTION

Discretionary fiscal policy has been studied from many perspectives since the era of Keynes

(e.g., Keynes, 1936; Kopcke et al., 2006; Chari et al., 2009; Farmer, 2009; Alesina, 2012;

Benhabib et al., 2014). An important issue is whether a government should intervene fiscally in

a recession, and if so, how. The answer will differ according to the cause and mechanism of

recession. Particularly, it will be different depending on whether “disequilibrium” is generated. The concept of disequilibrium is, however, controversial and therefore arguments continue even

now about the use of discretionary fiscal policy in a recession. In this paper, the concept of

disequilibrium is not used, but instead the concept of a “Nash equilibrium of a Pareto inefficient

path” is used.

Recessions are generated by various shocks (e.g., Rebelo, 2005; Blanchard, 2009;

Ireland, 2011; Schmitt-Grohé and Uribe, 2012; McGrattan and Prescott, 2014; Hall, 2016).

Some fundamental shocks will change the steady state, and if the steady state is changed

downwards (i.e., to lower levels of production and consumption), households must change the

consumption path to one that diminishes gradually to the posterior steady state. Therefore,

growth rates become negative; that is, a recession begins. However, the explanation of the

mechanism of this type of recession is not perfect because an important question still needs to

be answered. If households discontinuously increase (“jump up”) their consumption from the

prior steady state to a point on the posterior saddle path and then gradually move to the posterior

steady state, Pareto efficiency is held and thereby unemployment rates do not rise. Therefore,

even in a serious and large-scale recession, unemployment does not increase. This is a very

unnatural outcome of a serious recession.

Harashima (2004, 2009, 2013a) showed a mechanism by which households do not

jump up their consumption even if the steady state is changed downward because they are

intrinsically risk averse and non-cooperative and want to smooth consumption. The

consumption jump does not give them the highest expected utility; that is, unsmooth and

discontinuous consumption is not optimal for households. Hence, instead of choosing the

posterior saddle path, they will choose a “Nash equilibrium of a Pareto inefficient path” as the

optimal consumption path. Because of its Pareto inefficiency, unemployment rates will increase

sharply and stay high during a recession. This paper examines whether discretionary fiscal

policy is necessary, and if it is necessary, how it should be implemented when an economy is in

a recession and proceeding on such a Pareto inefficient path.

Fundamental shocks that change the steady state basically mean shocks on deep

parameters. A representative fundamental shock, an upward shock on the rate of time preference

(RTP), is examined in this paper. Faced with this shock, a government has three options: (1) do

not intervene, (2) increase government consumption, and (3) cut taxes. The consequences of

these options are examined and the outcomes are evaluated to determine which is the best

option. I conclude that increasing government consumption until the demand meets the present

level of production and maintaining this fiscal policy during the recession is the best option.

Nevertheless, this option will be accompanied by large and accumulating government debts, but

these debts can be sustained if the government properly increases taxes in the future. This option

means that huge government debts will play an essential role as a buffer against negative effects

of the fundamental shock.

2 A MECHANISM OF RECESSION

2.1 An upward RTP shock There are various possible sources of recession, but in this paper, a recession caused by a

fundamental shock, particularly by an upward shift of RTP, is examined because an upward

shift of RTP seems to be most likely the cause of the Great Recession (Harashima, 2016). A

2

technology shock was probably not the cause of the Great Recession because technology does

not suddenly and greatly regress. Frictions on price adjustments are also unlikely to be the cause

because the micro-foundation of friction does not seem to be sufficiently persuasive (e.g.,

Mankiw, 2001), particularly the micro-foundation of its persistence. On the other hand,

Harashima (2016) showed that an upward RTP shock could explain the occurrence of the Great

Recession and showed evidence that the estimated RTP of the United States increased in about

2008.

RTP plays an essential role in economic activities, and its importance has been

emphasized since the era of Irving Fisher (Fisher, 1930). One of the most important equations in

economics is the steady state condition

rθ 

where θ is RTP and r is the real rate of interest. This condition is a foundation of both static and

dynamic economic studies. The mechanisms of both θ and r are equally important. Particularly,

RTP is an essential element in expectations of economic activities because RTP is the discount

factor for future utility. In addition, RTP has been regarded as changeable even over short

periods (e.g., Uzawa, 1968; Epstein and Hynes, 1983; Lucas and Stokey, 1984; Parkin, 1988;

Obstfeld, 1990; Becker and Mulligan, 1997). Furthermore, households behave based on the

expected RTP of the representative household (RTP RH) (Harashima, 2014, 2016). That is,

changes in RTP and the expected RTP RH can be an important source of economic fluctuations.

2.2 The model The model in this paper is based on the models in Harashima (2004, 2009, 2013a) and assumes

non-cooperative, identical, and infinitely long living households, and that the number of

households is sufficiently large. Each of the households equally maximizes the expected utility

   dtcuθtE t 

 0

0 exp

subject to

  tt t cA,kf

dt

dk  ,

where yt, ct, and kt are production, consumption, and capital per capita in period t, respectively;

A is technology and constant; u is the utility function;  tt kAfy , is the production

function; and E0 is the expectations operator conditioned on the agents’ period 0 information set.

yt, ct, and kt are monotonically continuous and differentiable in t, and u and f are monotonically

continuous functions of ct and kt, respectively. All households initially have an identical amount

of financial assets equal to kt, and all households gain the identical amount of income

 tt kAfy , in each period. It is assumed that  

0 t

t

dc

cdu and

  0

2

2

 t

t

dc

cud ; thus, households

are risk averse. In addition,  

0 ,

 



t

t

k

kAf and

  0

2

2

 



t

t

k

kf . Both technology (A) and labor

supply are assumed to be constant; that is, there is no technological progress or population

increase. It is also assumed that there is no depreciation of capital.

2.3 A Nash equilibrium of a Pareto inefficient path

3

tk

The prior steady state

before the shock on θ: W

The posterior steady

state after the shock

θ

Posterior line of 0 dt

dct

after the shock on θ

Line of 0 dt

dkt

Z

Pareto inefficient transition

path

Prior line of 0 dt

dct

before the shock on θ

Pareto efficient

saddle path after

the shock on θ

Pareto efficient saddle

path before the shock

on θ

The effects of an upward shift in RTP are shown in Figure 1. Suppose first that the economy is

at steady state before the shock. After the upward RTP shock, the vertical line 0 dt

dct moves

to the left (from the solid vertical line to the dashed vertical line in Figure 1). To keep Pareto

efficiency, consumption needs to jump immediately from the steady state before the shock (the

prior steady state) to point Z. After the jump, consumption proceeds on the Pareto efficient

saddle path (the posterior saddle path) from point Z to the lower steady state after the shock (the

posterior steady state). As a result, negative economic growth rates continue for a long period,

but unemployment rates will not increase and resources will not be destroyed or left idle. Note

that an increase in household consumption means consuming the part capital indicated by the

gap between the posterior saddle path (the thin dashed curve) and production (the bold solid

curve) for each kt, which initially is the gap between point Z and W.1

Figure 1: An upward RTP shock. All terms are defined in the text.

tc

1 If depreciation of capital is assumed to exist, the “consumption” of excess capital will be achieved by a reduction of investments that correspond to depreciated capital and an increase in consumer goods and services.

0

4

However, this discontinuous jump to Z will be uncomfortable for risk-averse

households that wish to smooth consumption. Households may instead chose a shortcut and, for

example, proceed on a path on which consumption is reduced continuously from the prior

steady state to the posterior steady state (the bold dashed line), although this shortcut is not

Pareto efficient. The mechanism for why they are very unlikely to jump consumption is

explained in Harashima (2004, 2009, 2013a) and also in the Appendix. Because households are

risk averse and want to smooth consumption, and are also intrinsically non-cooperative, they

behave strategically in game theoretic situations. Because of these features, when households

strategically consider whether or not the jump is better for them (i.e., they are in a game

theoretic situation), they will generally conclude that they obtain a higher expected utility if they

do not jump. Hence, households will not actually choose this path and instead will choose a

different transition path to the steady state (e.g., the bold dashed curve). Because this transition

path is not on the posterior saddle path, it is not Pareto efficient (I call this transition path a

“Nash equilibrium of a Pareto inefficient path” or more simply a “Pareto inefficient transition path”). Therefore, the excess resources indicated by the gap between the posterior saddle path

(the thin dashed curve) and the Pareto inefficient transition path (the bold dashed curve) for

each kt (initially, the gap between points Z and X) will be destroyed or left idle. Unemployment

rates will increase sharply and stay high for a long period.

3 SHOULD THE GOVERNMENT FISCALLY

INTERVENE?

3.1 The government’s options

3.1.1 The three options When households choose a Nash equilibrium of a Pareto inefficient path, the government

basically has three options: (1) do not intervene, (2) increase government consumption, and

(3) cut taxes.

If Option (1) is chosen, the gap between the posterior saddle path and the Pareto

inefficient transition path (initially the gap between points Z and W) is not filled by any demand.

Therefore, unemployment rates increase sharply and huge amounts of resources are destroyed or

left idle. High unemployment rates and destruction of resources will continue until the economy

reaches the posterior steady state.

If Option (2) is chosen, government consumption is increased to fill the demand gap

between the posterior saddle path and the Pareto inefficient transition path, where government

consumption is indicated on a per capita basis similar to the other variables. Suppose for

simplicity that government consumption is zero before the shock. With increases in government

consumption, the path of the sum of government and household consumption (hereafter

“combined consumption”) can be equal to the posterior saddle path.

Conceptually, government consumption is the collective consumption of households

through government expenditures, for example, spending on various kinds of administrative

services that households receive. Therefore, increases in government consumption can be

substituted for decreases in household consumption. Nevertheless, government consumption

will not directly generate utility in households. In this sense, increases in government

consumption may be interpreted as forced increases in household consumption. Even if

households do not want these increases in government consumption, however, the increases will

work to increase aggregate demand. Option (2) therefore indicates a measure to compulsorily

fill the gap between aggregate demand and supply, even against households’ will, when the economy proceeds on a Pareto inefficient transition path. Notice that the excess resources

cannot be used for investments because the economy would otherwise deviate from a path to the

steady state.

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If Option (3) is chosen, households’ disposable incomes will increase, but if the

Ricardian equivalence holds, they will still proceed on a Pareto inefficient transition path.

Because household consumption does not change, high unemployment rates and destruction of a

huge amount of resources continue as in Option (1). Because there is a huge amount of excess

capital, no additional investment will be made. Nevertheless, if the Ricardian equivalence does

not hold, tax cuts may increase household consumption at least temporarily. Therefore, the

validity of Option (3) depends on the validity of the Ricardian equivalence. If households are

sufficiently rational, the Ricardian equivalence will basically hold at least in the long run.

Therefore, even if tax cuts are effective, they will be effective only in the short run, and these

short run effects will be reversed because the Ricardian equivalence will hold in the long run.

3.1.2 Financing In Option (3), tax cuts are financed by borrowing from households. In Option (2), an increase in

the government consumption is financed by borrowing from or tax increases on households.

Nevertheless, financing by borrowing will be preferred in Option (2) because the Ricardian

equivalence may not necessarily hold in the short run. If the Ricardian equivalence does not

hold, increases in taxes may increase unemployment rates and thereby the main aim of

Option (2) cannot be fully achieved. Therefore, it is highly likely that an increase in government

consumption will be financed by government borrowing, and therefore borrowing is assumed in

this paper. However, financing by borrowing requires tax increases in the future to pay off the

debt with interest. Options (2) and (3) assume that necessary future tax increases are fully

implemented by the government.

In addition, it is assumed that a government borrows money only from its own people,

that is, not from foreigners because foreign borrowing means that foreigners also intervene in

addition to the government, and such intervention is beyond the scope of this paper.

3.2 Comparison among options (1) Economic growth rate

Because production and consumption at the posterior steady state are lower than those at the

prior steady state, the rate of economic growth is equally negative during the transition in the

three options except for a subordinate option of Option (2), in which, as will be shown in

Section 4, it is zero. Nevertheless, there actually still will be steady technological progress

(remember that no technological progress is assumed in the model), and thereby the actual rates

of growth will not necessarily be negative or zero and may even be low but positive.

(2) Household utility

Households choose a Nash equilibrium of a Pareto inefficient path equally in the three options.

Therefore, the utilities of households are basically same in the three options.

(3) Unemployment

In Options (1) and (3), unemployment rates will rise sharply and stay high for a long period. In

contrast, in Option (2), high unemployment rates can be avoided because the gap of demand is

filled by increases in government consumption and thereby no resources are destroyed or left

idle.

(4) Government debt

In Option (1), government debt does not increase because the government does not borrow

additional money, but in Options (2) and (3), government debt will increase because of

continuous financing by borrowing. However, if taxes are raised properly to pay off the debt in

the future, government debt will stabilize in some future period.

3.3 Government debt

6

3.3.1 Is the government debt sustainable? The usual arguments on sustainable government debts (e.g., Hamilton and Flavin, 1986; Bohn,

1995) are not applicable to the government debts in Options (2) and (3) because households

proceed on an “unusual” Pareto inefficient transition path, so an alternative approach is

necessary. Let dt be per capita “extra” government debts in period t that are accumulated in

Option (2) or (3). Because all dt are owned by households as assumed above, dt also indicates

the financial assets of households, and the other household assets (other than dt) are ignored for

simplicity. In the future, dt is redeemed with interest, but the redemption takes a long time.

Because the Ricardian equivalence will hold in the long run, it is assumed that household

consumption is not influenced by dt. Let zt be per capita taxes to redeem a part of dt in period t

and also let gt be additional government borrowing in Option (2) or (3) in period t. In Option

(2),

ttt gcy  , (1)

and in Option (3),

ttt gcy  (2)

for any t because no new investment is made in Options (2) and (3) and the household assets

other than the government bonds are ignored; yt and ct are per capita income and consumption

of households in period t. If the condition

tttt zgdr  (3)

is satisfied indefinitely in a certain future period, government debt never explodes; that is, it is

sustainable where  10  tt rr is the real interest rate. By equality (1) and inequality (3), the

condition for sustainability in Option (2) is

tttttt zdrcy  . (4)

By inequalities (2) and (3), if inequality (4) is satisfied indefinitely in a certain future period,

government debt is also sustainable in Option (3).

Because the household assets other than dt are ignored, the sum of a household’s income and assets is

ttt cyd  .

If the sum of a household’s income and assets exceeds zt, that is, if

tttt cydz  , (5)

then zt can be imposed in the sense that households have enough resources to fully pay taxes.

Hence, by inequalities (4) and (5), if

ttt ddr  (6)

7

is satisfied, taxes that satisfy the condition for sustainable debts can be imposed. Here, because

10  tr , then inequality (6) always holds. Therefore, for any dt, there always exists zt that

satisfies inequality (3) indefinitely in a certain future period. That is, the government debt can

be sustainable for any dt, and even if dt becomes extremely large, the debt can be sustainable.

Consider an extreme example. If a government collects taxes that are equivalent to dt from a

household’s financial assets in a period, the government’s debts are eliminated completely all at

once. That is, any dt can be sustainable.

Such an extreme tax will not actually be imposed, but if dt exceeds a certain amount

such that

ttt zrdy  ,

(i.e., if taxes exceed income), then they need to be collected from a part of a household’s

holdings of dt. If households well know the possibility of a tax on dt in the future, they will not

regard their accumulated financial assets corresponding to dt as their “real” assets in the sense they can be freely used for consumption even though dt may be extremely large. In addition,

because any dt can be sustainable, the tax increase can be started even after all the excess capital

is eliminated. Hence, a huge amount of government debt can remain even if there is no excess

capital.

Finally, it is important to note that the increased tax revenues should not be used to

finance increases in government consumption for purposes other than deali