Capital Inflows: A Threat to Growth?

David Backus, Thomas Cooley, and Espen Henriksen

Restoring Growth in Advanced Economies NCAER, World Bank, & NYU | October 7, 2010

This version: October 9, 2010

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Capital inflows: sign of success?

Larry Summmers, IMF, October 3, 2004:

There is a standard set of things that finance ministers of countries with significant current account deficits say. Perhaps the sharpest formulation is: “We live in a country that capital is trying to get into. Would you rather live in a country that capital is trying to get out of?”

Capital inflows: portent of peril?

Daniel Gross, New York Times, May 8, 2005:

[US] imbalances are eerily reminiscent of recent economic crises. Could we see a perfect storm [for the US economy]? If so, what would it look like?

⋆ Nouriel Roubini estimates that long-term interest rates in the US could rise by 200 basis points over a few months and the value of the dollar would fall.

⋆ Said Barry Eichengreen: “The result would not be a full-blown financial crisis most likely, but it would still be a major recession.”

⋆ Adds Jeffrey Frankel, “some of us have been warning of this hard-landing scenario for more than 20 years.”

Facts about capital flows

What drives them?

▶ Business cycles ▶ Institutions ▶ Taxes and legal restrictions ▶ Commodity prices (oil) ▶ Political risk ▶ Exchange rates ▶ Anything that affects saving or investment

Some data to get us thinking...

Facts: current accounts Facts: net foreign assets Facts: current account spectrum Facts: summary

Capital flows are persistent Demography inherently persistent, too ⇒ Could it play a role in capital flows?

Facts: age distributions Facts: dependency ratios Facts: fertility Facts: life expectancy Facts: life expectancy Theory: economic structure

One-good world National production functions Unrestricted international capital flows Overlapping generations

▶ Fertility, mortality, immigration tied to data ▶ Fixed retirement age (65)

Result: demographic differences generate capital flows

Theory: capital flows implied by demography

[Coming soon!!]

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Capital flows revisited

An “imbalance” to be managed? A reflection of demography and life-cycle saving? Or something completely different?

Extra slides

US household net worth

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US personal consumption Model...

The economy consists of overlapping generations of ex ante identical agents who live up to I periods, with ages denoted by i ∈ I ≡ {1, …, I }.

At every point in time, there are I different cohorts alive. Individuals remain children for I_{0} periods. As children they neither consume, accumulate capital nor supply labor. After I_{0} periods the agents enter the economy as autonomous decision makers.

Demographics

The survival probability between age i and i + 1 is denoted s_{i,t} and varies with ages i and time. The unconditional probability of reaching age i is denoted s^{i} and is the product of conditional survival probability rates; s^{i} = ∏_{j=1}^{i−1} s_{j}.

Let x_{t} ∈ ℝ^{I} be the vector of number of members in each cohort in period t.

The demographic structure of the population changes through changes in fertility, mortality and immigration.

Let m_{t} ∈ ℝ^{I} be a vector with each element representing the cohort specific number of net immigrants at time t. Denoting Γ̂_{t} the matrix of deterministic fertility and mortality rates at time t, the law of motion for the population may be written

x_{t+1} = Γ̂_{t}x_{t} + m_{t}.
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Preferences and technology

Preferences of an agent born in period t may be summarized by a standard time-separable utility function with age specific weight β^{i}

E_{t+I_{0}} { ∑_{i=I_{0}+1}^{I}β^{i}s^{i}u_{i} (c_{i,t})},  (1)

where u_{i} is the instantaneous utility function, and c_{i,t} is consumption and leisure of an agent of age i in period t. The instantaneous utility function has the standard isoelastic specification

u (c_{i,t}) = \frac{(c_{i,t})^{1−σ} − 1}{1 − σ},

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Labor Supply

Each individual supplies labor inelastically to the market. The productivity and the rate of return on labor supplied changes with age according to a deterministic pattern. The vector of age specific efficiency units of labor is denoted {ϵ_{i}}_{i=1}^{I}. An easy way to exogenously capture childhood inactivity and old age retirement is to set labor efficiency for those cohorts equal to zero.

Extra slides

Production

Country j time t y_{j,t} = θ_{j,t}K_{j,t}^{α}N_{j,t}^{1−α}.

Equilibrium

Individuals in each country choose optimal quantities of capital supplied (saved) given prices. Combining the individuals’ intratemporal optimality condition with the period-by-period budget constraint gives the following second-order difference equation

a_{i+1,t+1} = a_{i,t}R_{t} + ϵ_{i}w_{t} + h_{t}−

(\frac{1}{βs_{i−1,t−1}R_{t}} )^{− \frac{1}{σ}} (a_{i−1,t−1}R_{t−1} + ϵ_{i−1}w_{t−1} + h_{t−1} − a_{i,t}).

Combined with the initial and terminal conditions, eq. (??), this uniquely defines the life-cycle savings (and consumption) sequence for given prices. Firms in each country choose optimal quantities of capital demanded given prices

K_{j,t}^{d} = (\frac{r_{j,t}}{αθ_{j,t}} )^{\frac{1}{α−1}} N_{j,t}.

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