New wine in old bottles: a meta-analysis of Ricardian equivalence.

• Author: Stanley, T.D.

1. Introduction

   This argument of charging posterity with the interest of our debt, or of relieving them from a portion of such interest, is often used by otherwise well informed people, but we confess we see no weight in it. (Ricardo 1820, p. 187)

   . . . (R)esults are all over the map, with some favoring Ricardian equivalence, and others not. (Barro 1989, p. 49)

   In recent years, there has been much discussion in Congress and the popular media (not to mention the academic journals) about the U.S. budget deficit, its effects, and possible elimination. To the clamorous cacophony of balanced budget rhetoric, Barro (1974) added a clear and reassuring note. Budget deficits do not matter; they affect neither aggregate demand nor the real interest. "(A) decrease in the government's savings (that is, a current budget deficit) leads to an offsetting increase in desired private savings, and hence to no change in desired national savings" (Barro 1989, p. 39). "This is the so-called Ricardian-equivalence theorem which states that it is economically equivalent to maintain a balanced budget or to run a debt-financed deficit, since the substitution of debt for taxes does not affect private sector wealth and consumption" (Leiderman and Blejer 1988, p. 2). It is the so-called Ricardian equivalence theorem (RET) because David Ricardo did not believe that people are indifferent to debt financing, Buchanan's (1976) claims and the label "Ricardian equivalence" to the contrary.(1)

   Needless to say, such a provocative proposition has attracted much discussion and empirical testing. Empirical testing, however, has had little impact on theoretical or policy discussions because the results are so mixed that they convince no one. Nonetheless, the conventional view expressed in the economic literature seems to be that the Ricardian equivalence is a "valid and useful proposition" (Leiderman and Blejer 1988, p. 29).(2) Or as Barro (1989, p. 48) states, "It is easy on theoretical grounds to raise points that invalidate strict Ricardian equivalence. Nevertheless, it may still be that the Ricardian view provides a useful framework for assessing the first-order effects of fiscal policy."

   The purpose of this paper is to provide a quantitative review (i.e., a meta-analysis) of the large number of empirical tests of Ricardian equivalence conducted over the last two decades. I endeavor to assess the wealth of empirical research on this provocative topic and to explain its vast variation. How sensitive is the empirical support for RET to the particular model specification? Does the amount of information utilized by a statistical test affect its results? Are models that pass additional specification tests more or less critical of Ricardian equivalence? Does the weight of empirical evidence support or reject Ricardian equivalence? In contrast to the conventional assessment that gives mild support for RET, our meta-analysis finds that strong evidence against Ricardian equivalence already exists in the literature. When adjusted for the statistical quality of a given test, the non-Ricardian effect becomes larger still.

2. A Meta-Analysis of the Ricardian Equivalence Theorem

   To find the genuine message in the noise, what we need are not just summaries of the literature, such as those found in the introductory chapters of dissertations and in most literature reviews, but also critical reviews. When empirical tests reach results that seem irreconcilable, a critical review survey should tell us which ones to disregard. . . . And even if it is not possible to weed out all the invalid evidence and to reconcile the rest, it should be possible to reduce the dissonance to a substantial extent. Meta-analysis reduces the effort required for such a critical survey and makes its results more specific. (Mayer 1993, p. 158)

   This study began with a review of the 110 references to "Ricardian Equivalence" found on EconLit's CD-ROM, 1980-1995.(3) From these, 28 empirical studies were identified (see Table 1). The only selective criteria used to identify these 28 empirical studies were whether the study claims to test Ricardian equivalence and reports the corresponding test statistic.(4) To avoid giving undue weight to dissertations and studies of potentially lower quality, each study is counted as a single test of RET, regardless of how many tests may actually be presented. For studies reporting multiple test results, a conventional model that uses the more sophisticated econometric method is selected. When there still remains more than one test, they are averaged. Several studies report Ricardo equivalence tests for multiple countries. Of course, these multinational studies often produce mixed results. However, if each test for each country is included, the evidence against RET strengthens. In any case, giving particular studies such a disproportionate weight is questionable, whether they represent the best or the worst the field has to offer. Better weighting schemes for a study's quality, reflecting proper statistical specification and greater statistical power, are employed in subsequent analyses.

   Standardizing RET Tests: Nonequivalent Effect Size

   The standard practice for testing Ricardian equivalence is to build an econometric model of consumption expenditures or interest rates (occasionally, exchange rates) and to estimate the model with and without the restrictions implied by RET For example, consumption is often estimated by

   [C.sub.t] = [[Alpha].sub.0] + [[Alpha].sub.1][Y.sub.t] + [[Alpha].sub.2][Y.sub.t-1] + [[Alpha].sub.3][G.sub.t] + [[Alpha].sub.4][W.sub.t] + [[Alpha].sub.5][Tx.sub.t] + [[Alpha].sub.6][B.sub.t] + [[Alpha].sub.7][Tr.sub.t] + [[Epsilon].sub.j], (1)

   where [C.sub.t] is private consumption expenditures in quarter t, [Y.sub.t] is personal income, [G.sub.t] is government expenditures, [W.sub.t] is household net wealth, [Tx.sub.t] is government tax revenue, [B.sub.t] is government debt, and [Tr.sub.t] is government transfer payments. Given this formulation of the consumption function, RET may be interpreted as imposing the restrictions [[Alpha].sub.5] = [[Alpha].sub.6] = [[Alpha].sub.7] = 0 (Leiderman and Blejer 1988).(5) Parameter restrictions, consistent with RET, always form the null hypothesis. Although each researcher may choose a somewhat different model and differentially interpret the exact form of RET's parameter restrictions, the typical test of Ricardian equivalence is, nonetheless, a test of parameter restrictions.

   There is also considerable variation in the type of statistical test used in RET testing. Often the traditional F-test, or t-test for a single parameter restriction, is employed. Or more recently, Wald and Lagrange multiplier (LM) tests, both of which possess [[Chi].sup.2]-distributions, have become the popular choice. Such variation in test strategy and form presents an obstacle for smooth integration and summary of the empirical record.

   How can results of different studies using a variety of statistical tests be accurately compared and rationally accumulated and analyzed? I seek a reasonable method to compare and measure empirical results from different studies using different data sets, employing different models and relying on different statistical testing procedures. Toward this end, nonequivalent effect size (NEES) is defined.(6)

   Fortunately, useful approximations exist that can convert various statistical distributions - t's, F's, and [[Chi].sub.2]'s - to a common and meaningful metric, one that has a standard normal distribution. First, F-tests of parameter restrictions may be transformed using a normal approximation to the F-distribution that is not large sample bound (Abramowitz and Stegun 1964). Given a random variable f, which is distributed F([v.sub.1], [v.sub.2]) and is used to test a model's parameter restrictions, study i's nonequivalent effect size (NEES) is

   [N.sub.i] = [f.sup.1/3](1 - 2/9[v.sub.2]) - (1 - 2/9[v.sub.1])/[(2/9[v.sub.1] + [f.sup.2/3] 2/9[v.sub.2]).sup.1/2]. (2)

   [N.sub.i] has an approximate standard normal distribution N(0, 1) (Abramowitz and Stegun 1964).(7) In the case of t-tests, they can be converted to F-distributions with [v.sub.1] = 1 by squaring. The resulting F's may, in turn, be further transformed by Equation 2.

   Similarly, Wald and LM tests, [[Chi].sup.2] distributions with v degrees of freedom, can be approximated by a standard normal variable,

   [N.sub.i] = [([[Chi].sup.2]/v).sup.1/3] - (1 - 2/9v)/[(2/9v).sup.1/2] (3)

   (Abramowitz and Stegun 1964). These normal approximations are so accurate that they can be used to extend standard statistical tables (e.g., Levin and Rubin 1991). Even for small degrees of freedom, they are often accurate to [+ or -]0.01. In this way, all types of RET tests may be measured on the same scale, [N.sub.i].

   [N.sub.i] is a common metric, measuring the strength of the evidence against Ricardian equivalence or debt neutrality (i.e., nonequivalent effect size, NEES). The larger a positive [N.sub.i], the stronger the evidence against RET is. Negative values reflect a smaller than expected test statistic. If Ricardian equivalence is an accurate description of the effect of government deficits, NEES will be approximately zero. Given this common denominator, RET tests can be directly compared and combined using conventional descriptive and inferential statistics. Even those statistical methods that explicitly demand normality (e.g., regression analysis) are appropriate.

   Methods

   To assess the overall strength of the evidence against RET, the average nonequivalent effect size [Mathematical Expression Omitted] may be calculated (where L is the number of studies). To determine whether the literature contains a statistically significant nonequivalent effect, the statistic [Mathematical Expression Omitted] may be compared to 1.96 because each [N.sub.i] is a standard normal variate under the null hypothesis of RET. If Ricardian equivalence were true, [[Mu].sub.N]...