Demography and International Capital Flows^{∗}

David Backus,^{†} Thomas Cooley,^{‡} and Espen Henriksen^{§}

April 19, 2011 Work in progress

Abstract

We consider the causes of international capital flows. Since capital flows are extremely persistent, we argue that their drivers must be persistent, too. We think the most compelling candidates are, in order, demographic trends, movements in productivity, and policies (like tax policy) that change slowly over time. We explore these ideas in a multi-country overlapping generations model in which saving decisions are tied to agents’ life expectancy. Capital flows reflect differences between saving and investment across countries, which themselves reflect differences in demography. The sharp differences in age profiles across countries generate substantial capital flows on their own. Productivity and productivity growth play smaller roles. Capital taxes, which we use as a “wedge” to account for differences in capital-output ratios across countries, affect the level of net foreign asset positions but have a relatively small impact on flows. We conclude that demography plays a central role in the substantial international flows of capital we observe in the modern economy.

JEL Classification Codes: F21, J21.

Keywords: current account balances, net foreign asset positions, life-cycle saving, mortality, fertility, productivity, capital taxes.

∗Preliminary and incomplete: no guarantees of accuracy or sense. We welcome comments, including references to related papers we inadvertently overlooked.

† Stern School of Business, New York University, and NBER; dbackus@stern.nyu.edu.

‡ Stern School of Business, New York University, and NBER; dbackus@stern.nyu.edu.

§ Norwegian Pension Fund Global; espen.henriksen@gmail.com.

1 Introduction

In the 1920s capital began flowing from Massachusetts to North Carolina, a process that continued until after World War II. This movement of capital was linked to the migration of the textile mills of New England to the South. In the 1950 capital moved again, as textile manufacturing moved from the US to Mexico, India, and Malaysia. The movement of capital from less productive to more productive uses is a story repeated over and over again throughout history and around the world. Whether capital moves within a country — say from Massachusetts to North Carolina — or between countries — say from the US to Mexico — its flow addresses imbalances between local sources of funds (savings) and uses (investment). The period from 1880 to 1913 is often described as the golden era of capital mobility.

Through much of history, the major capital flows have been from rich countries to poorer ones. The London markets, for example, financed canals in the US and railroads from Australia to India. The standard theory, articulated clearly by Lucas (1990), is that capital should flow from rich countries to poor countries because the returns to capital should be higher in the latter.

The suggestions that capital should flow from rich countries to poor ones in pursuit of higher returns have both been challenged by the evidence. Ohanian and Wright (2010) have shown that the direction of capital flows was not always consistent with the pursuit of higher returns as they measured them. Even more damning is the evidence of recent history, in which the most notable importer of capital has been the richest country, the United States. Australia, Spain, and the UK have also been importers of capital. Germany, Japan, China, and Switzerland have been significant exporters of capital. Over the last ten years, oil-exporting countries, including many developing countries, have been massive exporters of capital.

These facts are collectively referred to as “global imbalances.” The standard view in policy circles is that they represent not a sensible market reallocation of capital but a threat to economic stability. Such “imbalances” are “unsustainable” and the longer they last, the more drastic and painful will be the ultimate “adjustment.” We don’t find this line of thought persuasive. For one thing, the US current account has been in deficit for most of the last twenty-five years, averaging more than 4% of GDP over the last decade. If there’s peril in the situation, it’s been a long time coming. Some of the same people now argue that these capital flows were a significant cause of the financial crisis of 2007-2009. [Commented out Bernanke, had a different point I think.] The short-hand version goes something like this: Capital exporting countries flooded the US with savings, looking for safe returns. Many of them purchased not equity or textile mills, but US government and agency debt and shares in money market funds. These flows — and loose monetary policy — kept interest rates low, making it easy for US individuals and financial institutions to leverage themselves. Portes (2009), for example wrote: “I maintain that global macroeconomic imbalances are the underlying cause of the crisis[. ...] The underlying problem in international finance over the past decade has been global imbalances, not greed, poor incentive structures, or weak financial regulation, however egregious and important these may be.”

It is certainly true that capital has flowed to the US in large quantities. The reasons are many: the US dollar’s status as the reserve currency, the depth, liquidity and relative safety of US financial markets; good institutions. But, it is very difficult to make a causal connection between capital flows and the financial crisis. For one thing the geography of the crisis did not fit this claim. The crisis was severe for some capital importing and some capital exporting countries The financial crisis has everything to do with the decisions financial institutions made about what to invest in and little to do with capital flows.

In this paper we are concerned with what drives international capital flows. We begin by arguing that the very nature of net foreign asset positions gives us valuable clues about what to look for. In the next section of the paper we document some of the striking features of foreign asset positions. These show that net foreign asset positions have very significant low frequency components which means that they are dominated by factors that have slow moving trends. What are they? In this paper we argue that most compelling candidates in order are demographic (occasionally mentioned but largely ignored) trends, movements in productivity, and factors (like tax policy) that influence the capital output ratio.

The natural vehicle to study capital flows is multi-country overlapping generations model where individuals make savings decisions based on their conditional life expectancy and capital flows between countries. In such a world individuals will decide their life cycle savings and consumption based not only on domestic birth rates and mortality but also on the demography of other countries as well. Changes in fertility and mortality are key to understanding and modelling capital flows. As fertility declines populations get older, as mortality declines ( life expectancy increases) the ratio of years of work to years of retirement declines. Global capital flows act to equilibrate the demand and supply of global savings.

We study a calibrated general equilibrium model with a rich set of demographics. We ask to what extent can net foreign asset positions be explained over time (and hence capital flows) by demography, productivity differences and differences in the policy wedges that determine capital output ratios. Differential demographic trends drive savings and investment differences as workers adapt to increased life expectancy and decreased fertility. In such a world capital flows to countries with more favorable demographics and demographics explain well the differences in net foreign asset positions observed in the data. Differences in productivity explain some but not a lot of the movements in net foreign asset positions over time. Differences in wedges due to taxes and other frictions are important in accounting for differences in capital levels but not capital flows.

In the next section of the paper we describe the features of capital flows and net foreign assets that are the subject of controversy. The following section describes the salient characteristics of fertility and mortality that we believe are important drivers of capital flows. We then describe and multi-generation, multi-country overlapping generations model which describes savings decisions in our model economy. We explain the modelling of demographics and the definition of equilibrium. Section 5 describes the results of three major exercise the determine the role of demographics, productivity differences and tax wedges on net foreign assets. We compare the implications of our model with the actual data and find strong support for the view that demographics are an important driving force in global capital flows.

2 Facts: capital flows and net foreign asset positions

Global capital flows are most often depicted by plotting the current account — aggregate investment minus aggregate savings — as a fraction of GDP. Figure 1 is a plot of current account balances for a number of countries.

What is striking about this picture is the persistence of current account positions. Countries that tend to have current account deficits, the U.S., the U.K. and Australia, have them for a long time and likewise for countries that have current account surpluses - e.g. Germany, Japan and China. The net foreign asset positions of these countries are shown in Figure 2 below.

In principal these should represent the same phenomena and the Current Account should simply represent the change in Net Foreign Assets. In practice they don’t line up and the difference is the subject of exploration. Ricardo Hausmann and Federico Sturzenegger (xxxx) have argued that this difference is ”dark matter” that is explained by unmeasured flows of intellectual property. McGrattan and Prescott (2009) have argued that it is technology capital and plant specific intangible capital that explains the differences and accounts for much of the measured differences in asset returns. For our purposes these are secondary issues and we will focus primarily on Net Foreign Assets and will treat changes in Net Foreign Asset positions as the capital flows of interest.

Although much attention has been directed at the flows of capital as represented by the current account statistics, not enough has been directed at the question of why these data display the characteristics that they do. The features of the data belie the frequently voiced worry about sudden reversal of capital flows. Figure 3 3 is the spectra of current account flows for a group of six countries including both capital exporters and capital importers over the time period 1960-2008.

The spectra are completely dominated by the low frequencies reinforcing the conclusion that capital flows are driven by long term factors.

3 Facts: demography

The current account for a country is simply the difference between domestic savings and domestic investment. It is natural to look at life-cycle considerations as primary drivers of domestic savings. For a country the key drivers are fertility and mortality. The former determines how many workers there are over time and the latter determines how many years of post-employment [??] they have to save for. As fertility declines as it has in many of the most important economies, there are fewer workers saving over time. As mortality declines the number of years of retirement for each worker is likely to increase relative to the number of years of work.

Figure 4 shows the fertility rates for Europe, the United States, Japan, China, and India. There is a remarkable convergence of fertility rates over time but only the United States and India have fertility above replacement rate. Figure 5 shows how fertility breaks down across the various parts of Europe. While fertility has been decreasing, life expectancy has been increasing. Indeed their has been a remarkable convergence of poor countries and wealthy countries in terms of life expectancy at birth. Figure 6 shows the life expectancy for Europe, the United States, Japan, China, and India, while Figure 7 shows the differences across Europe. There has been very strong convergence across most of Europe but Eastern Europe has lagged far behind.

The convergence across the world is easily seen by plotting the distribution of life expectancy over time for the complete set of countries in the U.N. data set. In the earliest year, 1965, the distribution was bi-modal with a large mass of countries having very low life expectancies. Over time the distribution has not only shifted to the right but more of the mass of the distribution has shifted to the right meaning there are fewer countries that have really low life expectancy. This is at least one indication of development success.

The combination of increasing life expectancy and decreasing fertility means that the median age of the populations increasing, in some cases dramatically. Figure 9 shows the median age for Europe, the United States, Japan, China, and India, Figure 10 shows the breakdown for Europe.

These demographic trends will influence the world demand and supply for capital. Technology and institutions are obviously important drivers of capital flows but to the extent that capital is free to flow between countries lifecycle considerations in these countries will influence capital flows. To quantify the effects demographic dynamics have on savings, investment, the rates of return on the factors of production, and, finally, capital flows, we calibrate a two-country general equilibrium model with very detailed demographic dynamics. In the next section of the paper we describe the basic overlapping generations structure and the demographic transitions.

4 A model

To quantify the effects demographic dynamics have on savings, investment, rate of return on the factors of production, and, finally, current account, we calibrate a two-country general equilibrium model with fine demographic dynamics.

4.1 Demographics

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.

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. According to time and age specific fertility rates φ_{i,t}, in each period these individuals give birth to a certain number of new individuals, and the number of newborns in period t + 1, x_{1,t+1}, is the product of x_{t} and the vector of fertility rates φ_{t}. Then the law of motion of a population with survival rates as given above, but deterministic fertility, can be described by a simple (I × I) matrix^{1}

Γ̂ = (\begin{matrix}φ_{1} & φ_{2} & φ_{3} & ⋯ & φ_{I} \\ s_{1} & 0 & 0 & ⋯ & 0 \\ 0 & s_{2} & 0 & ⋯ & 0 \\ ⋮ & ⋮ & ... & ... & ⋮ \\ 0 & 0 & ⋯ & s_{I−1} & 0 \end{matrix}) ,

where the diagonal elements (s_{1}, …, s_{I−1}) are the conditional survival probabilities.

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}.

1The largest eigenvalue of the matrix Γ is the rate of growth of the population in steady state regardless of the initial condition. The eigenvector corresponding to this eigenvalue describes the share of each age group in the steady state population.

4.2 Preferences and technology

4.2.1 Individuals’ optimization

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},

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.

There are at least two ways of taking care of accidental bequests and by that closing the model. On alternative is to do like Storesletten, Telmer and Yaron (2000), Rios-Rull (2001) and others, where each agent has written a contract with the members of it’s own cohort that make the survivors share the wealth or debts of those who die prematurely. This way of closing the model do, however, eliminate the risk element by disturbing the intertemporal price of capital and the result is that the Euler equation and policy function makes the model very close to a model with no surivial/death probability.^{2}

An alternative way to close the model where the individuals still face mortality risk is by dividing total aggregate bequest equally on all inhabitants. Agents may accumulate assets in positive and negative amounts. The agent maximizes utility subject to the budget constraint

c_{i,t} + a_{t+1,i+1} = a_{i,t} (1 + r_{t}) + ε_{i}w_{t} + h_{i,t},  (2)

2If h = (1 − s_{−1}) (1 + r) a_{−1}, then envelope condition wrt. the state variable a_{−1}, updated one period, is

∂v′ (a) /∂a = (1 + r′) (2 − s) [(1 + r′) a + wε′ − a′]^{−σ} , and the intertemporal marginal rate of substitution between consumption in two consecutive periods is equal to β (1 + r) (2 − s) s, with (2 − s) s > s for all 0 < s < 1. So “cohort specific insurance” is to close to entirely canceling out the effect of the death probability.

and the constraints following from the absence of a bequest motive

a_{1,t} = a_{I+1,t} = 0.  (3)

a_{i,t} is wealth, r_{t+i−1} is the spot market net rate of return of one unit of capital, w_{t+i+1} is the spot market price of one efficiency unit of labor, and accidental bequests, h_{t}, is the fraction of total inheritance or bequests that devolve on each individual alive at time t

h_{t} = \frac{H_{t}}{∑_{i=I_{0}}^{I} x_{t}} ,

where

H_{t} = ∑_{i=I_{0}}^{I} (1 − s_{i}) a_{i,t}.

In order to close the model and limit the heterogeneity, immigrants who enter the economy are assumed to have the same stocks of human and physical capital stock as the existing members of their cohort. The physical capital stock is assumed transferred from the members of their own cohort.

Hence, individuals maximize (1) subject to (2) and (3).

4.2.2 Production

Country j time t

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

4.3 Equilibrium

1. 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. (3), this uniquely defines the life-cycle savings (and consumption) sequence for given prices.

2. 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}.

3. Quantities are aggregated across countries and prices are set such that aggregate

quantity demanded equals aggregate quantity supllied. For country j at time t

K_{j,t}^{s} = ∑_{i=I_{0}}^{I} a_{i,j,t}.

and

R_{t} : ∑_{j} K_{j,t}^{d} = ∑_{j} K_{j,t}^{s}

5 Calibration / parametrization

Parameter Target  Value
β  …  1.0
σ  …  4
α  …  0.33
δ  …  5 · .025

6 Results

6.1 Benchmark 6.2 Differences in TFP

– matching relative GDP

6.3 Differences in capital wedges

– matching K/Y ratios

7 Parameter values and wealth-age profiles 8 Properties of the benchmark model 9 Productivity and capital taxes 10 China A Appendix

A.1 Capital-output ratios

The capital stock K is constructed with the perpetual inventory method from time series data on real investment from the Penn World Tables, using a depreciation rate of 0.06. Following what is now standard practice, we compute the initial capital stock K_{0}as I_{0}/ (g + δ), where I_{0} is the value of the investment series in the first year it is available and g is the average geometric growth rate for the investment series between the first year with available data and 1971. See Caselli (2005) and Caselli and Feyrer (2007.

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flows,” International Economic Review 47, 1013-1032. Henriksen, Espen, 2002, “A demographic explanation of US and Japanese current account

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Lane, Philip, and Gian Maria Milesi-Ferretti, MA paper. Lane, Philip, and Gian Maria Milesi-Ferretti, 2007, “The external wealth of nations mark

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Figure 1 Current account balances in select countries

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Figure 2 Net foreign asset positions in select countries

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Figure 3 Spectra for current account balances

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Figure 4 Fertility...

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