Solving the Feldstein-Horioka Puzzle With Financial Frictions

That average investment rates rise strongly with average savings rates across countries, which they still do: 0.52 with a standard error of 0.06 in a 64-country sample over 1960-2003. The original estimate, from 16 OECD countries over the 15 years 1960-1974, was 0.89 with a standard error of 0.07 (Section 2). The authors’ update covers 64 countries for 1960-2003 and finds “the FH coefficient is 0.52 with a standard error of 0.06. Although lower than the original estimate, it is still positive and significantly different from zero.” The result is robust across cuts: 0.67 for the 16-OECD subsample over the full period, 0.60 for the full sample over 1960-1974, and 0.46 over 1974-2003. One measurement caveat is disclosed in a table note: “The new data source produces an FH coefficient different from Feldstein and Horioka’s original estimate for the same sample.” The authors summarize the empirical literature as having left the finding standing: “Across empirical studies, however, the FH coefficient has remained large and significant, although it has tended to decline in recent years.”

Savings and investment rates average about 21 and 22 percent of GDP, correlate at 0.77 across countries, and have cross-country standard deviations of 0.07 and 0.04; the coefficient is the product of that correlation and that dispersion ratio. The decomposition the authors write down – the coefficient equals the correlation of the two average rates times the ratio of the investment-rate standard deviation to the savings-rate standard deviation – matters because a model can go wrong on either leg (Section 2). In the data, “the average savings rate has a larger standard deviation than the average investment rate: 0.07 versus 0.04. These two rates have a correlation of 0.77.” Two further facts anchor the calibration: “countries that grow faster not only invest more, but also save more on average. In particular, the correlation of the average growth rate of GDP per worker with the average investment rate is 0.47 and that with the average savings rate is 0.31.” And on flows: “The average of the absolute current-account-to-GDP ratios, referred to as the capital flow ratio for simplicity, is 7% for the 64 countries over the full period. The average of the absolute foreign-asset-position-to-GDP ratios is 49%. International financial markets over this period do not seem to have enabled countries to reap the long-run gains from intertemporal trade.”

A continuum of small open economies, each a one-sector Cobb-Douglas production economy with an idiosyncratic total factor productivity shock, no aggregate uncertainty, and a benevolent government choosing allocations. Following Clarida, the continuum device lets the authors “study a large number of countries in a tractable fashion.” All economies produce a homogeneous good usable for consumption or investment; productivity has a common deterministic growth component and a country-specific Markov shock; and allocations are normalized by labor and the common growth rate (Section 3.1). The two frictions are stated as restrictions on international financial markets: “One is limited spanning: the menu of available assets is restricted to noncontingent bonds. The other is limited enforcement: countries have the option to default and the extent to which countries can be penalized is restricted to a reversion to costly financial autarky.”

Standard preference and technology parameters matched to US equivalents, a 1.4 percent output loss on default from Tomz and Wright, and a three-regime switching autoregressive productivity process estimated by maximum likelihood on 64 countries’ TFP series. Risk aversion is 2, the discount factor is 0.89 “to match the U.S. average real capital return of 4% per annum,” depreciation is 10 percent per year and the capital share 0.33 (Section 3.3). The discount factor is recalibrated for each alternative model to hold the interest rate at 4 percent – 0.96 in the frictionless model, 0.955 in the enforcement model and 0.94 in the bond model with natural limits – so that differences across models reflect frictions rather than rates. The productivity process is designed around three documented features of the 64 TFP series: a wide range of levels (“the average TFP difference between the United States and Senegal is more than 13 times the cross-country average of time-series standard deviations”), higher volatility in poorer countries (“the mean of the coefficients of variation of the TFP series is 0.02 for OECD countries and is 0.04 for developing countries”), and abrupt subperiod shifts (Peru’s coefficient of variation and mean were “0.02 and 3.8 before 1980, and 0.05 and 3.5 after 1980”). The estimated three-regime process has all regimes persistent “with ρ around 0.99,” with the middle regime the most volatile, and the authors justify the number of regimes on fit grounds: “The three-regime specification greatly improves the goodness of fit over the two-regime specification, while introducing another regime barely improves the goodness of fit.” Simulation matches the data’s dimensions: “in each simulation we obtain 64 series of 44 periods from the invariant distribution,” with 1,000 simulations.

A Feldstein-Horioka coefficient of −0.01 and enormously excessive capital flows – and the authors claim verifying Feldstein and Horioka’s conjecture in a quantitative model is new. “Feldstein and Horioka made their conjecture long before there existed quantitative stochastic general equilibrium models that could be used to evaluate it. In this subsection, we verify the Feldstein-Horioka conjecture in a standard complete markets model” (Section 4.1), and the conclusion states the claim plainly: “Our work first shows that this finding is a puzzle for the frictionless (complete markets) model. To our knowledge, this point is new to the literature.” The magnitudes: “The frictionless model generates a large capital flow ratio, 62%, which is about 9 times that in the data. The average foreign-asset-position-to-GDP ratio is also large, 6.12, which is about 12 times that in the data.” The reason for the near-zero coefficient runs through the decomposition: “Under a persistent shock process, investment depends on changes of TFP shocks: a country with a higher average TFP growth rate invests more on average. Savings depends not on changes, but on levels of shocks: a country with a higher average TFP level saves more on average,” and since changes and levels of a persistent mean-reverting process are slightly negatively correlated, the average savings and investment rates correlate at −0.09 while the relative dispersion is small.

It holds and strengthens as persistence falls: dropping the autoregressive coefficient from 0.999 to 0.5 moves the coefficient from −0.001 to −0.12. The authors trace the logic: “As the persistence decreases, the correlation between changes and levels of shocks becomes more negative, and the dispersion of changes relative to levels rises. Thus, the correlation between the average investment and savings rates becomes more negative, and the relative dispersion of the two rates rises with lower persistence. As a result, the FH coefficient becomes more negative.” The illustration uses an AR(1) with innovation standard deviation set at 4.2 percent “to match the unconditional standard deviation of the TFP data,” and the conclusion is stated conservatively: the coefficient falls “from −0.001 to −0.12, but the FH puzzle remains” (Section 4.1). A definitional sensitivity is also flagged: “If savings is defined as national savings instead of domestic savings, the FH coefficient will be zero,” because fully diversified portfolios make national income and consumption constant over time while investment still varies.

No, and the authors flag the failure against Lucas’s paradox. Sorting countries by wealth and growth, “Rich, fast-growing countries on average both invest and save a lot, while poor, stagnant countries on average both invest and save little. Even under complete markets, these two types of countries have relatively low capital flows. Rich, stagnant countries on average save a lot but invest little, and poor, miracle countries on average save little but invest heavily. Thus, capital flows generally move from rich, stagnant to poor, miracle countries. This prediction is not observed in the data, as pointed out by Lucas (1990)” (Section 4.1).

Because with a full set of contingent assets the option to stay in markets is so valuable that default is unattractive, so the endogenous limits are loose – countries can borrow three times their income. “Given the volatile shock process and the benefit of trading contingent claims, the default penalties of permanent exclusion and output losses make continuation in international financial markets highly attractive. Countries therefore have little incentive to default. Consequently, the model implies large capital flows and a close-to-zero FH coefficient” (Section 1). Quantitatively the enforcement model gives a coefficient of −0.01, a capital flow ratio of 0.56 and a foreign-asset-to-output ratio of 4.1, “both of which are much higher than those in the data.” The state-contingent limits “are larger for countries with larger capital stocks or higher TFP shocks because they have less incentive to default,” and “are very loose when compared with the noncontingent debt limits in the two-friction model. On average, countries can borrow three times their income” (Section 4.2). Investment behaves much as under frictionless markets (correlation with output growth 0.83) while savings barely responds (0.10), so the two average rates stay nearly uncorrelated.

All the way to no output loss and immediate re-entry, which still leaves the coefficient at 0.23 while capital flows fall below the data – and they argue the penalties needed would be unrealistic. Reducing the output loss has small effects: “Even under a zero output drop, the enforcement model still produces an FH coefficient close to zero and a large volume of capital flows” (coefficients of −0.015, −0.011 and −0.009 for output losses of 2.0, 0.9 and 0 percent). Allowing partial exclusion helps more but not enough: as the re-entry probability rises to 20, 40 and 100 percent the coefficient rises to 0.08, 0.11 and 0.23 while the capital flow ratio falls to 0.02, 0.07 and 0.10. “Even when η approaches 100%, the enforcement model still generates an FH coefficient much lower than that found in the data. The capital flow ratio and the dispersions of the savings and investment rates, however, are much lower than those found in the data. To produce the observed FH coefficient, we would need an even lower default penalty: countries can access the markets with some probability in the defaulting period and with certainty in the next period. This seems unrealistic” (Section 4.2). The empirical anchor cuts the other way: “Gelos, Sahay, and Sandleris (2004) documented that, on average, defaulting countries are excluded from international financial markets for 5 years, which implies an η of 20%.”

That a bad shock can raise capital and investment, because contingent enforcement constraints bind in good states and relax in bad ones. “In this model, the demand for capital decreases when shocks are bad or when enforcement constraints are binding. With contingent assets, the enforcement constraints tend to bind under good shocks and relax under bad shocks. Bad shocks thus have two effects: they decrease capital due to lower returns, but increase capital due to the relaxation of the enforcement constraints. Hence, capital and investment might increase when countries are hit with bad shocks if the effect of relaxing the binding enforcement constraints is large enough.” This is not just an aesthetic problem: it mechanically holds the Feldstein-Horioka coefficient down, because such a country ends up with “a high investment rate and a low savings rate in response to the bad shock,” which “lowers the standard deviation of the average investment rate and the savings-investment correlation across countries, and dampens the increase in the FH coefficient” (Section 4.2).

Natural debt limits barely bind, so flows stay large and the coefficient small (0.05); imposing tighter ad hoc limits does reproduce the data, but the limits are then assumed rather than derived. With natural limits, “these debt limits are loose enough such that only a small fraction of countries bind at the constraints in equilibrium,” and the model gives a coefficient of 0.05 with a capital flow ratio of 0.38 (Section 4.3). Precautionary saving under incomplete markets does change savings behaviour – “the correlation between the average savings rate and average output growth increases from zero in the frictionless model to 0.41 in the bond model” – but the dispersion problem remains: “the dispersion of the savings rate is still much larger than that of the investment rate: 0.34 versus 0.04. This is because the amount of borrowing is virtually unrestricted: the foreign-asset-position-to-GDP ratio is 5.6, which is much higher than 0.49 in the data.” Following Castro’s ad hoc constraint limiting borrowing to a fraction of beginning-of-period resources, “we find that when κ is set at 9.8%, the bond model reproduces the observed FH coefficient,” with implications otherwise similar to the two-friction model. The authors credit and then criticize this route: “Castro’s analysis shows that we need debt limits to be severe enough to restrict capital flows close to the data to resolve the FH puzzle. Although this is an important contribution, Castro’s analysis leaves the source of the borrowing constraints unexplained. Our work suggests that the interaction of the two financial frictions could be a potential source for these required borrowing constraints.”

It makes them noncontingent and tighter, for two separable reasons. The endogenous limit “specifies the maximum amount of debt that can be supported without default under all future contingencies,” as a function of the current shock and next period’s capital stock. The two tightening mechanisms are distinguished: “First, these debt limits have to ensure that countries prefer to repay, even under the worst realization of the TFP shock. Second, the benefits of staying in the markets are considerably lower when the only available asset is a noncontingent bond. Countries thus have a greater incentive to default, implying that the debt limits are tighter” (Section 1, restated in Section 4.4: “market welfare is lower in the two-friction model than in the enforcement model because limited spanning restricts trading opportunities, although the autarky utilities are the same across these two models”). The limits are increasing in capital “because poor countries have more incentive to default than rich countries,” and “overall allow countries to borrow about 30% of their output on average” (Section 3.4). One presentational caveat is noted honestly: a zigzag in the debt-limit-to-output figure “is the result of the numerical approximation.”

The Feldstein-Horioka coefficient, the volume and stock of capital flows, the savings-investment correlation, the dispersions of both rates, and the degree of risk sharing. “The bond-enforcement model generates an FH coefficient of 0.52, significantly different from zero and similar to that in the data. Thus, this model solves the Feldstein-Horioka puzzle” (Section 3.4). On flows: “the model generates a capital flow ratio of 10% and a foreign-asset-to-output ratio of 40%, which are close to their empirical counterparts of 7% and 49%.” On the correlation and dispersions: “the average savings and investment rates are positively correlated across countries with a correlation of 0.77, the same as that in the data. Also, the model produces small dispersions of savings and investment rates, similar to those found in the data; the standard deviations are 0.06 and 0.04, respectively.” The authors also record where it does less well: the model “generates positive correlations between the output growth and the savings and investment rates, although these correlations are higher than those in the data,” and in the four-way comparison it “generates an average savings rate closest to the data, although it underperforms with regard to the average investment rate” (Section 4.4). On risk sharing: “international risk sharing is far from perfect empirically, which is completely at odds with the perfect risk sharing prediction of the complete markets model. The enforcement model and the bond model with the natural debt limits still provide too much risk sharing relative to the data. With the tight debt limits, the bond-enforcement model greatly reduces risk sharing across countries and generates a degree of risk sharing that is much closer to that found in the data.”

Poor countries must save to invest because they cannot borrow; rich countries must invest at home because the interest rate discourages them from lending. “Countries with low capital face tight debt limits and cannot borrow much to invest when they are experiencing good productivity shocks: they have to save more to invest more. Countries with high capital intend to lend abroad when they are experiencing bad shocks. Nonetheless, total lending must be equal to total borrowing in equilibrium. These countries have to invest more at home because the interest rate decreases to lower their lending incentive. Consequently, the average savings and investment rates are positively correlated across countries” (Section 3.4). The second half of the mechanism is the removal of the enforcement model’s pathology: “the two-friction model does not have the counterfactual investment behavior in the enforcement model, even when the debt limits are tight. The key is that limited spanning makes repayments noncontingent. Repayments are more painful under bad shocks with lower income, and thus the enforcement constraints tend to bind when countries are hit with bad shocks. Therefore, investment tends to decrease in response to bad shocks as in the data” (Section 4.4).

Substantially: the coefficient ranges from 0.45 to 0.94 as the output loss falls from 2 percent to zero, and rises to 0.81-0.93 once partial re-entry is allowed, with capital flows falling correspondingly. With permanent exclusion only (zero output loss), “we find that capital flows are small and the FH coefficient is large” – 0.94 with a capital flow ratio of just 1 percent – which the authors explain as the mirror image of the enforcement case: “the exclusion from financial markets is less severe when only noncontingent bonds can be traded. Thus, to match the observed capital flows, we need the output loss as part of the default penalties. As the output drop parameter λ rises from 0 to 2%, the FH coefficient decreases from 0.94 to 0.45, but remains large and positive.” On partial exclusion at the benchmark output loss: “When the reentry probability is 20%, the model produces a small capital flow ratio of 4% and a large FH coefficient of 0.81. Capital flows decrease and the FH coefficient rises as we further increase the reentry probability” (Section 4.4). So the benchmark calibration sits in a region where the result is genuinely parameter-dependent – the authors’ claim is that a plausible calibration delivers both targets, not that any calibration does.

That defaulters have debt fully written off and are treated on re-entry exactly like countries that never defaulted, both of which understate real-world penalties. “Note that in these experiments we assume that defaulting countries have debt fully written off and are treated the same after reentry as countries that have never defaulted. In the data, the default penalties are more severe because these assumptions are violated. Defaulting countries have only partial debt relief and need to repay a nonnegligible fraction of their outstanding debt when reentering the market” – with recovery rates of “40% for Ecuador’s 1999 default, 36.5% for Russia’s 1998 default, and 28% for Argentina’s 2001 default” – “In addition, though defaulting countries regain access to markets, they may have only limited access and face a higher cost of borrowing relative to nondefaulting countries. If we enrich the enforcement model further along these dimensions, the default penalty will increase, which loosens borrowing limits and lowers the FH coefficient” (Section 4.2). The same caveat is repeated for the two-friction model, so it cuts against the authors’ own headline number as well as against the enforcement-only case.

Because every version of the model, frictionless or not, produces a positive time-series savings-investment correlation, so that correlation cannot discriminate between them. “All of our models produce a positive time-series correlation independently of financial frictions because both savings and investment respond positively to persistent TFP shocks. This is consistent with the findings of Baxter and Crucini (1993) and Mendoza (1991). The cross-country correlation, however, does depend on financial frictions, which affect the ability of countries to borrow and the degree of divergence between the average savings and investment rates” (Section 1). Spelled out in Section 4.5: “One can imagine that in a world with a persistent shock process, each country could have positively correlated savings and investment rates over time, but might have very different average savings and investment rates. In this study, we have shown that the degree of divergence depends on the ability of countries to borrow and lend, which in turn is given by the degree of financial frictions.” Two implementation notes accompany the time-series exercise: capital adjustment costs of the standard quadratic form must be added, “calibrated to match the volatility of investment in the data,” and “we did not impose the capital adjustment cost in the enforcement model, due to technical complexity.”

Well on volatilities and on the cyclicality of consumption and investment, and badly on the countercyclicality of net exports. “The bond-enforcement model generates fluctuations of output, consumption, and net exports close to those observed in the data. It also comes close to matching the cyclical behavior of consumption and investment. In addition, the model generates a cross-country output correlation that is the same as the consumption correlation due to limited risk sharing under the tight endogenous debt limits. These tight constraints, however, also limit the model’s ability to generate the countercyclicality of net exports found in the data” (Section 4.5). The statistics are computed to match the data treatment: logged and Hodrick-Prescott filtered annual series for 1960-2003, averaged across 1,000 simulations of 64 series over 44 periods.

Because their shock process is more volatile and their multi-country setting offers more insurance opportunities, so both the need and the scope for borrowing are larger. “Kehoe and Perri (2002) … found that limited enforcement severely restricts capital flows when default penalties consist of permanent exclusion from financial markets but no drop in output. In contrast, we find under the same default penalties that limited enforcement barely restricts capital flows. The difference comes from two sources. First, our shock process is more volatile than theirs. We calibrate to TFPs of both developed and developing countries, while they calibrate to those of developed countries only. Second, our multicountry model offers more insurance opportunities than their two-country model. Thus, in our model, there is both a greater need and a greater opportunity to insure, which leads to larger capital flows” (Section 1). A second methodological difference is with Zhang’s earlier endogenous-debt-limit work: “In his setup, the debt limits depend only on exogenous endowment shocks and are independent of agents’ choices. In contrast, in our production economy, the debt limits depend on both exogenous shocks and endogenous capital stocks. Thus, countries affect the debt limits they face through their choices of capital stocks.”

As filling a near-vacuum: the authors count few theoretical studies, and note that the leading ones have been refuted or address a different question. “Relative to the vast empirical literature, there are few theoretical studies on the FH finding. Westphal (1983) argued that the FH finding is due to official capital controls. This finding, however, has persisted even after the widespread dismantling of capital controls. Obstfeld (1986) argued that population growth might generate a savings-investment comovement in a life-cycle model. Summers (1988), however, showed that the FH finding persists even after controlling for population growth. Barro, Mankiw, and Sala-I-Martin (1995) showed in a deterministic model that the savings and investment rates are perfectly correlated under full capital mobility after countries reach steady states. We instead show in a stochastic model that these two rates are uncorrelated under full capital mobility” (Section 1).

Predictive content about how savings, investment and flows respond to changes in default penalties or contracting technology, which an exogenous-limits model cannot supply. “Understanding the source of debt limits is important if one is interested in how savings, investment, and capital flows respond to changes in default penalties or contracting technologies” (Section 1), and again in the conclusion: “In this work, the limited enforcement friction endogenizes borrowing constraints and links them to the fundamental parameters of the default penalties. This analysis is useful for predicting international capital flows when the underlying [environment changes].” The summary claim for the paper as a whole is comparative rather than absolute: “our work analyzes the roles of different financial frictions in one harmonized framework and highlights the importance of the interaction between the two frictions” (Section 5).