Do finite horizons matter? The welfare consequences of capital account liberalization

That the infinite-horizon Hicksian measure divides a welfare difference generated in the first decade or two by a discount sum running to infinity, and so reports a small number for a gain that is not small when it arrives (§1, §3.2). The authors set the question up against Gourinchas and Jeanne (2006): “If agents are infinitely-lived, the increase in consumption (welfare) brought about by liberalization may not be quantitatively important over the infinite lifetime consumption path,” but “if the lion’s share of the welfare benefits from liberalization accrues over relatively short horizons, and in the early years after policy implementation, then calculating the welfare benefits over a finite horizon may be more appropriate, and policy-relevant.” The arithmetic is made explicit later: the welfare difference entering the finite-horizon and infinite-horizon formulas is literally the same quantity, “because the only gain in welfare occurs before convergence; autarkic and integrated consumption streams from t* to T are equal.” What differs is only the geometric discount sum used to convert it into a per-period percentage, and “[t]he farther out consumption is in the future, the more it is discounted making the value of mu small.”

A standard infinite-horizon Ramsey model with Cobb-Douglas production, in which liberalization lets the economy jump immediately to the steady-state capital stock implied by the world interest rate (§2). “Raw labor grows at the population growth rate n. Labor-augmenting technical change grows increases the ratio of effective labor to raw labor at a rate of g. The rate of pure time preference is rho,” with discount factor beta = 1/(1+rho) and depreciation delta. The autarkic economy accumulates capital according to its Euler equation until it reaches its own steady state; “[a] financially integrated economy faces the world interest rate, R*_w, directly upon liberalization. Capital flows into the liberalizing economy and the steady state k*_w is reached instantly.” The authors state the simplification openly: “This setup assumes that an economy instantaneously converges to its steady state when it opens up. We make this assumption to abstract from speed of convergence issues.”

Only faster – and this is a scope condition worth holding on to, because it is more conservative than the informal case for liberalization (§2). The baseline imposes absolute convergence: “we assume that the autarkic interest rate converges to the world interest rate meaning that the autarkic economy eventually reaches the same steady state level of capital as the liberalized economy.” Hence “[b]ecause of this, the steady state of the autarkic economy is the same as the steady state of the rest of the world,” and “capital account liberalization serves to expedite an economy’s movement towards its own (world) steady state.” All of the measured welfare gain is therefore a timing gain: consumption is higher during the years the autarkic economy would still have spent climbing. The permanent level effect the authors describe in the introduction is relative to the pre-liberalization starting point, not relative to the counterfactual autarkic economy’s own eventual steady state.

Two normalisations of the same welfare difference (§3.1-3.2). The infinite-horizon measure mu is “the percentage increase in lifetime consumption it would take to equate the welfare of the autarkic economy to that of the liberalized economy,” with welfare computed as the discounted sum of log consumption weighted by population growth, yielding mu = exp[(1 - betan)(U_int - U_aut)] - 1. Substituted for a horizon T, the same construction yields mu_T = exp[((1 - betan)/(1 - (betan)^(T+1)))(U_int - U_aut)] - 1. The authors spell out why the ordering is mechanical rather than substantive: “Since betan < 1 we know that (1 - betan) < (1 - betan)/(1 - (beta*n)^(T+1)); therefore, mu < mu_T.” Read against the finite-horizon question the paper wants to ask – “in the first ten years, what is the percent change in autarkic consumption that agents would need to be compensated in order to not implement the policy?” – mu “underestimates the short run benefits of liberalization.”

A conventional annual calibration and initial capital taken from observed 1995 data for 81 non-OECD countries (§3.1, Table 1). The parameters are beta = 0.96, capital share alpha = 0.3, depreciation delta = 0.06, output growth g = 1.012, population growth n = 1.022, and coefficient of relative risk aversion gamma = 1 – log utility, consistent with the log form used in the welfare sums. “Using the population weighted average capital stock in 1995 as the initial level of capital, the autarkic economy will climb from the resulting initial level of capital, 1.96, to the steady state level of capital, 3.97,” with the optimal path computed “by Euler equation iteration in the de-trended version of the representative agent problem.” Elsewhere the paper reports that this calibration implies a world interest rate R* of “approximately 5.42%.” The appendices list the countries sorted into quartiles “by Capital to Output Ratio in 1995.”

A five-year average gain of 19.02 percent of annual consumption against minus 3.46 percent at the infinite horizon, for the same underlying welfare difference (§3.2, Table 2). “For the sample of 81 non-OECD countries, the infinite horizon average mu is -3.4642% increase in annual consumption. This means that the cost of financing financial liberalization outweighs the benefit of a short run increase in consumption. In contrast, the five year finite horizon mu_T is an order of magnitude higher at 19.0225%.” Table 2 traces the decline across horizons – 12.49 percent at 10 years, 7.89 at 15, 4.82 at 20, 2.71 at 25, 1.21 at 30, 0.11 at 35, then negative from 40 years on – which is what the authors mean by “consistent with theory mu declines as the autarkic consumption path converges to its steady state value.” The timing claim underlying all of this is that “95% of the increase in annual consumption from capital account liberalization accrues in the first 10-15 years after the opening.”

Gains scale with initial capital scarcity, and the most capital-abundant non-OECD countries are made worse off even in the short run (§3.2, Table 2). “Table 2 also shows that the magnitude of the finite horizon increase in welfare represented by mu_T is directly proportional to the size of the capital gap between autarky and integration. … For the highly capital-scarce countries in the first quartile of initial capital stock values k_0, the finite horizon mu_T at five years is a 51.47% increase in annual consumption. For non-OECD countries that are relatively more capital-abundant, the five year finite horizon mu_T is a decline in annual consumption of -0.90% for countries in the fourth quartile of initial capital stock values.” The mechanism is the same one that drives the average: a country already near the integrated steady state borrows little, gains little in consumption, and still owes interest.

The horizon pattern survives but the levels fall, because some countries are converging to a lower steady state than the world’s (§4.1, Table 3). Instead of a common world interest rate, the authors use country-specific earnings-price ratios from the Emerging Markets Data Base as the capitalisation rate, which “allows for cross country heterogeneity, in educational attainment, fertility decisions, technology, and institutions, that would make the steady state levels of capital of countries differ.” The sign of the effect relative to the baseline depends on the premium R*_i - R*: “[w]hen the premium is negative, the steady state level of capital that the country is converging to is higher than the world steady state level of capital. Liberalization will allow these countries to reach that higher steady state of capital faster. The opposite is true when the premium is positive: … [u]pon liberalization this country will converge to a lower steady state and it will experience lower welfare than under the assumption of absolute convergence.” The average numbers are 9.89 percent at five years, 2.68 at ten, and minus 8.35 percent at infinity.

Enough to flip the sign of the infinite-horizon answer, which is the paper’s own most striking caveat (§4.2, Tables 2, 4, 5). The baseline is deliberately unfavourable: “the infinitely-lived economy services the capital it borrows from the rest of the world … as interest payments in perpetuity. Here, the principal is never paid off,” and the per-period cost is (k* - k_0)(1 - R*). Replacing it with the Obstfeld-Rogoff formulation, imposing the transversality condition so that “both the principal and interest are paid off at infinity,” raises the average five-year gain to 29.32 percent and, crucially, makes the infinite-horizon average positive at 4.97 percent – “the welfare gains here are positive even at infinity (except for initial capital stocks in the fourth quartile)” – because “[i]f the repayment occurs far enough into the future, it will not affect welfare in a drastic way.” A 50-year equal-amortisation contract, by contrast, front-loads repayment and gives 18.22 percent at five years but minus 4.12 percent at infinity. The authors draw the general lesson themselves: “the way financing costs are repayed greatly influences the welfare effect of financial liberalization. If the bulk of the repayment occurs far enough into the future the short run welfare gain will be larger. … When measuring welfare using a short run horizon, these effects will be amplified.”

Yes, and in the direction the mechanism predicts (§4.2, Table 6). “We also conduct the welfare analysis by initiating the autarkic economy using initial capital stock values from 1960 rather than 1995 (GJ formulation). By 1995 a number of countries had already implemented capital account liberalization policies. Therefore characterizing the capital stock values for non-OECD economies in 1960 may be a more realistic representation of economies in autarky.” With an average initial capital level of 1.81, the five-year average gain rises to 32.03 percent and the infinite-horizon average becomes positive at 1.47 percent, with 59.59 percent at five years for the first quartile. The authors treat this as confirmation rather than surprise: “[t]his is not surprising since the size of the capital gap for most non-OECD countries was much larger in 1960.”

That state-contingency in the financing instrument is worth roughly the whole gain – but the exercise is explicitly illustrative, and its debt case relies on a crude device for handling negative consumption (§4.3, Tables 7-9). The authors add a technology shock “normally distributed with mean 1 and standard deviation 0.03,” stating plainly: “While this is not a realistic shock, it is used for illustrative purposes.” With no repayment at all the five-year average is 21.87 percent and the infinite-horizon average 1.49 percent. With a non-contingent debt contract requiring (k* - k_0)(1 - R*) every period, the computed figures are large and negative at every horizon (minus 44.77 percent at five years, minus 74.38 percent at infinity) – but that calculation is made “assuming no default translated here as forcing c > 0, if c <= 0 I put c=0.05 a negligible amount, but it serves the purpose of calculating,” so the magnitude reflects that flooring convention as much as the economics. With an equity contract, under which “the economy does not make payments during times with negative shocks” and default is assumed away, the five-year average is 26.30 percent and the infinite-horizon average 1.47 percent, so that “an equity contract comes close to the case of an economy that liberalizes and does not need to make repayment.”

No. The claim is about how to measure a policy of this shape, and it is explicitly not a claim that level effects matter more than TFP effects (§5). “This paper studies the transitional dynamics of a policy change that leads to a temporary growth effect. We find that that the methodological approach to measure the welfare impact of a policy change like capital account liberalization can drive the magnitude of policy effect estimates.” The authors then bound the claim: “We do not claim that policies that lead to permanent effects on TFP and growth are not important. We simply point out that policy changes that lead to temporary growth but permanent level effects of this sort (like capital account liberalization) can add up to significant increases in levels of per capita incomes. Examining the welfare consequences of a temporary growth (and permanent level) effect is also the more consistent way of testing the predictions of the neo-classical growth model in the context of capital account liberalization.” The verb used for the finite-horizon recommendation is consistently “may be more appropriate,” not “is correct.”

By arguing the regressions test the wrong prediction (§1). “Research on the macroeconomic impact of capital account liberalization finds few, if any, robust effects of liberalization on real variables such as investment and GDP per capita,” citing the Edison et al. (2002) and Kose et al. (2006) surveys, “[b]ut it is a mistake to view the prevailing null effect findings as conclusive because most of the research papers in this area employ cross-sectional regressions designed to test whether liberalization produces permanent differences in the long-run growth rates of the economic variables of interest. In contrast to these tests for permanent effects of liberalization, theory predicts that liberalizing the capital account will have a temporary impact on growth rather than a permanent one [Henry (2007)]. Therefore, cross-sectional regressions that do not find permanent growth effects of liberalization do not undermine the predictions of the neo-classical model.” The supporting theoretical point is that “permanent growth effects are caused by an increase in TFP changes and in the context of the neo-classical growth model, TFP changes are independent of the capital account regime.”