Question

Secular stagnation refers to a situation where the growth rate in technological improvement declines dramatically (or even falls to zero). Suppose the economy is initially in a steady state and the rate of technological progress falls.

Suppose that after secular stagnation occurs, policymakers realize that the economy is below the golden-rule capital stock per effective worker. They subsequently introduce policies to encourage additional saving. Assume the economy success-fully adjusts to the golden-rule steady state. Outline the conditions that must hold for this level of capital per effective worker to be maintained. How does the growth rate in consumption per worker in this steady-state compare to the steady-state that was obtained prior to increased saving?

Answer 1

Keynes (1936) explained how an economy can be depressed due to a lack of demand.

Indeed, if householdsí demand for consumption and Örmsí demand for investment are

excessively low, then the economy fails to produce at full capacity. While the resultingdepressions are usually seen as an extreme manifestation of a business cycle phenomenon,

Hansen (1939) was the Örst to worry that it might be a permanent state of a§airs. This

is the "secular stagnation" hypothesis.

When aggregate demand is weak, ináation declines and the central bank responds by

aggressively cutting the nominal interest rate such as to stimulate demand. However,

a fundamental constraint on monetary policy is that the nominal interest rate cannot

be negative. Indeed, no-one is willing to pay more than $100 for a bond yielding $100

in the future. In the mid-1990s, Japan was the Örst large industrialized country to hit

the zero lower bound and to fall into the liquidity trap. Its subsequent history, with

an economy mired in very low ináation and weak GDP growth, suggests that there is

no mechanism through which an economy naturally recovers from a persistent lack of

demand. Moreover, Japan is facing a policy conundrum as aggregate demand remains

desperately weak despite a budget deÖcit of about 7% of GDP, a debt-to-GDP ratio of

230%, and substantial monetary accommodation.

Over the past few years, there has been growing concerns that the U.S. and the Eu-

rozone might be in a similar situation as Japan. In particular, Summers (2014) has

emphasized that the credit boom of 2003-2007 in the U.S. did not generate a correspond-

ing economic boom, which suggests that the unsustainable demand for consumption of

poor borrowers was hiding an already weak level of demand of rich lenders.

Despite the prominence of the secular stagnation hypothesis in the policy debate,

there has been few attempts to model it explicitly. In this paper, I o§er a simple theory

of secular stagnation, on which I then rely for a careful policy analysis. The structure

of the model is a Ramsey economy with money and áexible prices, to which I add three

features.

First, I assume that the central bank imposes a ceiling on ináation. This, together

with the zero lower bound on the nominal interest rate, generates a lower bound on the

real interest rate. In most industrialized countries, central banks never allow ináation to

exceed 2%, which prevents the real interest rate from ever falling below -2%.

Second, I assume that households derive utility from holding wealth. This can raise

their propensity to save to such an extent that a negative real interest rate is necessary

for the economy to produce at full capacity. Importantly, lived households

should be interpreted as dynasties. Hence, bequest motives are important determinants

of the saving behavior of households. In particular, we know that pure altruism alone

cannot account for the observed patterns of bequests. Instead, parents

seem to be commonly motivated by the "joy of giving". A "capitalist spirit" also induces

many individuals to derive intrinsic utility from the accumulation of wealth, which is then

passed on from generation to generation,1 While I rely forsimplicity on a representative household model, my results only require that a strictly

positive mass of households has a preference for wealth. Indeed, a well known result in

macroeconomics is that the real interest must eventually be determined by the behavior

of the most patient households. This is highly relevant as the rise in inequality is often

cited as a major cause of the recent decline in aggregate demand (Summers 2014). A

preference for wealth seems a natural explanation for the concentration of wealth in the

hands of a small number of households with a very low propensity to spend (Kumhof,

RanciËre and Winant 2015).

Finally, I impose a downward wage rigidity. If the ináation ceiling is su¢ ciently

low and the preference for wealth su¢ ciently strong, then aggregate demand is smaller

than aggregate supply. This reduces ináation, which raises the real interest rate, which

further contracts aggregate demand. To have a stationary secular stagnation equilibrium,

I therefore need to put a break on the deáationary spiral. This is achieved through the

downward wage rigidity.

In the secular stagnation equilibrium, aggregate demand is depressed. This induces

Örmsílabor demand to fall short of workersílabor supply. However, this ine¢ ciency is

primarily due to the lower bound on the real interest rate, not to the downward wage

rigidity. Indeed, if wages are more áexible, then ináation is smaller, the real interest

is higher, and the economy is even more depressed. Conversely, for a su¢ ciently high

ináation ceiling, there always exists a frictionless steady state equilibrium where the

economy produces at full capacity.2

The obvious policy response to secular stagnation is to raise the ináation ceiling.

However, in most countries, this seems politically and institutionally out of reach. Hence,

I explore alternative remedies. A simple policy analysis conÖrms that the usual set of

tools used for macroeconomic stabilization are not adequate in the context of secular

stagnation. Increasing the money supply through open market operations is useless in a

liquidity trap. A helicopter drop of money that is su¢ ciently large to induce the economy

to produce at full capacity is inconsistent with the ináation ceiling. A Öscal stimulus raises

Örmsídemand for labor much more than workersíconsumption level. Hence, it is likely

to be welfare reducing, even though the government spending multiplier is typically well

above 1.

However, with a wider set of policy instruments, the government can implement the

Örst-best allocation of resources without raising the ináation ceiling. To understand this result, note that secular stagnation is fundamentally due to an excessively high real interest rate. This creates two distortions. First, it raises the cost of capital. This

reduces the demand for investment, resulting in depressed capital-labor ratio. Second, a high real interest rate reduces the demand for consumption. The distortion should

be addressed by subsidizing the income from physical capital. This can either be achieved

through an investment subsidy or a reduction in the taxation of corporate income. The

second distortion can be ofset through a wealth tax, which reduces the efective real

interest rate faced by consumers. This policy is revenue neutral and it exactly replicates

the allocation of resources that would result from an increase in the ináation ceiling.

By inducing the economy to produce at full capacity, the optimal policy makes the

price level proportional to the money supply. Hence, to prevent a jump in the price level

upon implementation of the policy, the government must redeem the money supply that

is not used for transactions. This suggests that relying on the printing press to

some stimulus can eventually make the government reluctant to implement the optimal

Representative Household Model

• Households

Time is continuous. There is a mass 1 of inÖnitely lived households. Each household

consumes a quantity ct of a single consumption good with price Pt

. It supplies labor lt

paid at nominal wage Wt and receives a real lump-sum transfer t

. The nominal wealth

At of a household is composed of physical capital Kt

, government bonds Bt

, and money

Mt

:

At = P

K

t Kt + Bt + Mt

; (1)

where P

K

t denotes the nominal price of capital. Firms pay Rt to rent capital from

households. Capital depreciates at rate . There are three components to the nominal

return from a unit of physical capital: the rent Rt

, the loss due to depreciation P K

t

, and

the capital gain P_ K

t

. Bonds yield a nominal return it

, while money yields a zero nominal

return. The wealth of the representative household therefore evolves according to:

A_

t =

h

Rt

The intertemporal budget constraint prevents households from running Ponzi schemes: