53383625
Volatility and Growth: Governments are Key
There exists a persistent disagreement in the literature over the effect of business cycles on economic growth. This paper offers a solution to this disagreement, suggesting that volatility carries not only a positive direct effect, but also a negative indirect effect, operating through the insurance mechanism of government size. Theoretically, the net growth effect of volatility is then ambiguous. The paper reveals the underlying endogeneity of government size in a balanced panel of 90 countries from 1961 to 2010. In practice, the negative indirect channel dominates in democracies, but with less power to choose public services in autocratic regimes the positive direct effect takes over. Consequently, volatile growth rates are detrimental to growth in democracies, but beneficial to growth in autocracies. The empirical results suggest that a one standard deviation increase of volatility lowers growth by up to 0.52 percentage points in a democracy, but raises growth by 1.66 percentage points in a total autocracy. These findings point to a crucial intermediating role of governments in the relationship between volatility and growth. Both the size of the public sector and the regime form assume key roles.
152350717
Cross-Country Evidence on the Link between Volatility and Growth
This paper presents empirical evidence against the standard dichotomy in macroeconomics that separates growth from the volatility of economic fluctuations. In a sample of 92 countries as well as a sample of OECD countries, we find that countries with higher volatility have lower growth. The addition of standard control variables strengthens the negative relationship. We also find that government spending-induced volatility is negatively associated with growth even after controlling for both time- and country-fixed effects.
153775801
How Robust is the Empirical Link between Business-Cycle Volatility and Long-Run Growth in OECD Countries?
It has been argued that business-cycle volatility dampens growth. This paper argues that this is no stylised fact. A review of the literature reveals that arguments in favour of no, or even a positive, impact of business-cycle volatility on growth are as convincing as the arguments pointing in the other direction. Empirical evidence using annual data for 24 OECD countries from 1960 to 2000, based on robust cross-country regressions and panel models, raises doubts about a clear negative impact of volatility on growth. Moreover, the hypothesis of Granger-non-causality of business-cycle volatility for growth cannot be rejected.
153909204
Is There a Core of Usable Macroeconomics We Should All Believe In
Real output in most advanced capitalist economies fluctuates around a rising trend. One can argue about whether it is best to think about that trend as passing through successive cyclical averages, defined in one way or another, or best to think of it as passing through cyclical peaks, or some other measure of "potential" output. While the outcome of that argument has consequences for macroeconomic theory, I will bypass it for now. The important observation is that, on the whole, the observed fluctuations around trend are contained within a moderately narrow corridor. Unemployment rates tend to run between, say, 5 percent and 10 percent in the United States. (Other countries have different typical ranges, and in each of them, the range can shift from time to time. It is important, theoretically and practically, to understand why; but that remains an open question.) There are notable exceptions to this generalization, of course, the most famous being the depression of the 1930's; but they are exceptions. Again it is important to know why fluctuations are so contained. This could reflect some natural equilibrating process, or it could reflect the intervention of automatic or discretionary government policy, or it could be a mixture of both. That is another issue on which opinions differ. I think it is part of the usable common core of macroeconomics that the trend movement is predominantly driven by the supply side of the economy (the supply of factors of production and total factor productivity) and that the appropriate vehicle for analyzing the trend motion is some sort of growth model, preferably mine. Now, what about those fluctuations around the trend of potential output? A moment ago I put the normal range of unemployment rates at 5-10 percent. By Okun's law I am talking about fluctuations of real GDP with an amplitude of 8-10 percent or so from peak to trough-contained, but not trivial. In my picture of the usable common core of macroeconomics, those fluctuations are predominantly driven by aggregate demand impulses, and the appropriate vehicle for analyzing them is some model of the various sources of expenditure. I am not so obtuse as not to have observed that the whole point of "real-business-cycle theory" is the assertion that these short-run motions of the economy are in fact supplydriven. But my view is that this explanation has been an empirical failure, or at best a nonsuccess. There are now two possibilities. As for the first, I entertain the hope that flexible, observant members of the real-business-cycle school, like Martin Eichenbaum and his coworkers, have come more or less to the same conclusion, and they have found ways to open up the fabric of their underlying model so that it will allow-or insist-that demand-side impulses play the dominant role in short-run macroeconomic fluctuations. Then this proposition is indeed part of the usable core of macroeconomics, and economists can go on to argue back and forth about the best way of modeling those demand-side forces. The other case is that the situation is as before, and the real-business-cycle school holds monolithically to the view that short-run fluctuations are just optimal supply-side adjustments to unforeseeable shocks to tastes and * Department of Economics, Massachusetts Institute of Technology, Cambridge, MA 02139.
17349861
The link between volatility and growth: Evidence from the States
We present evidence on the relationship between output volatility and growth using state data. No evidence of such a relationship is found once other correlates of growth are incorporated into the analysis. This finding contradicts published results using international data; some possible explanations for the contradictory results are discussed.
154459114
On the link between volatility and growth
A model of growth with endogenous innovation and distortionary taxes is presented. Since innovation is the only source of volatility, any variable that influences innovation directly affects volatility and growth. This joint endogeneity is illustrated by working out the effects through which economies with different tax levels differ in their volatility and growth process. We obtain analytical measures of macro volatility based on cyclical output and on output growth rates for plausible parametric restrictions. This analysis implies that controls for taxes should be included in the standard growth-volatility regressions. Our estimates show that the conventional Ramey–Ramey coefficient is affected sizeably. In addition, tax levels do indeed appear to affect volatility in our empirical application.
154082261
Productivity growth and the Structure of the Business Cycle
Over recent years `opportunity cost' (OC) models of growth have been constructed which suggest that firms take advantage of the possibility of intertemporal subsitution in order to engage in productivity-improving activities during recessions. This paper tests whether this argument is correct, using a semi-structural vector autoregression to distinguish the trend from the cycle. The results are mildly supportive of the OC theory. Demand shocks tend to have a negative impact on productivity, both in the short and long run, and the short-run impact is stronger in those countries where fluctuations are more transitory. There is no evidence, however, of a significant R&D response to demand shocks.
153726175
Virtues of bad times: interaction between productivity growth and economic fluctuations
We develop a model of optimal productivity growth under demand fluctuations. We consider two alternative hypotheses. First, we assume that productivity growth is costly in terms of current production. Second, we assume that the cost of productivity improvements is independent of current production. It is shown that, in the first case, productivity improvements will be countercyclical whereas, in the second case, they will be procyclical. The model then is used to study the impact of the frequency and amplitude of fluctuations on long-run growth. The results corresponding to the first hypothesis are shown to be consistent with recent empirical work.
155007172
Uncertainty and Optimal Consumption Decisions
linear production function, that for some utility functions the optimal initial consumption in the random case decreases for all values of initial wealth as compared with the initial consumption in the deterministic case. For other utility functions the optimal consumption always increases. Hence it seems, from these examples, that two divergent forces are at work. The first is the desire to consume more initially as a hedge against the uncertain future. The second force is the desire to consume less initially so as to increase the future consumption prospects. (It is assumed, of course, that increased inputs increase outputs for all possible random events, or states of the world). The relative strength of each of these forces, as implied by the utility function, is the key to the relationship between random consumption and deterministic consumption in this model. The major conclusion of this paper is that the qualitative difference between optimal consumption decisions in the two different models is very strongly influenced by the shape of the utility function. In particular the third derivative of the utility function plays a rather large role. It is this derivative that determines the attitude toward the skewness of a distribution in the theory of portfolio choices, as may be seen from the analysis of Pratt [7] and Tobin [10]. Even in these models, however, the third derivative cannot be ignored, since ignoring skewness distorts the results. Moreover, there does not seem to be any intuitive economic reason to make any assumptions concerning the third derivative of the utility function. The extent to which the utility function influences savings and consumption decisions is exhibited in a precise manner. It may be shown that the qualitative relationship between random and deterministic consumption depends in general on the initial wealth. It is not true, as one would infer from the papers cited above, that random consumption is always either greater than or less than deterministic consumption independently of the initial wealth. In other words, for many utility functions the initial wealth turns out to be a decisive factor in the qualitative relationship between the random and deterministic case. Naturally this relationship will also normally depend on -the probabilistic structure of the model. The key result of this paper is a theorem which gives a necessary and sufficient condition for determining the qualitative relationship between random consumption and deterministic consumption. This condition, which is both necessary and sufficient, is in a particularly simple form in that it depends only on the known parameters of the model (i.e., the production function, the utility function, and the distribution of the random variable) and also on the optimal deterministic policy which, in general, is much simpler to exhibit than its counterpart in the random case.
154073000
The effects of wage volatility on growth
This paper shows that the volatility of wages has significant effects on a country’s rate of economic growth. Our theoretical framework suggests two distinct channels in which wage volatility affects growth: a positive direct way and a negative indirect way. The direct effect stems from precautionary savings, whereas the indirect effect works through the mediating role of government size. In the empirical part, we use a 3SLS approach to analyze a panel of 20 high-income OECD countries and find strong evidence for the existence of both effects. These results carry general and specific implications. In general, ignoring indirect effects operating through government size may mask the real net effects of volatility on growth, which could result in misleading conclusions. Specific to wage volatility, our results suggest that the net effect on economic growth depends on both government size and the wage premium from working in the private sector. Within our sample, we find evidence for both – countries for which wage volatility is beneficial to growth and others for which it is detrimental.
154783354
Sources of economic growth
Abstract For 116 countries from 1965 to 1985, the lowest quintile had an average growth rate of real per capita GDP of - 1.3%, whereas the highest quintile had an average of 4.8%. We isolate five influences that discriminate reasonably well between the slow-and fast-growers: a conditional convergence effect, whereby a country grows faster if it begins with lower real per-capita GDP relative to its initial level of human capital in the forms of educational attainment and health; a positive effect on growth from a high ratio of investment to GDP (although this effect is weaker than that reported in some previous studies); a negative effect from overly large government; a negative effect from government-induced distortions of markets; and a negative effect from political instability. Overall, the fifted growth rates for 85 countries for 1965–1985 had a correlation of 0.8 with the actual values. We also find that female educational attainment has a pronounced negative effect on fertility, whereas female and male attainment are each positively related to life expectancy and negatively related to infant mortality. Male attainment plays a positive role in primary-school enrollment ratios, and male and female attainment relate positively to enrollment at the secondary level.
67752995
Human Capital and Growth
This paper describes a growth model with the property that human capital accumulation can account for all observed growth. The model is shown to be consistent with evidence on individual productivities as measured by census earnings data. The central hypothesis is that we learn more when we interact with more productive people.
153712070
Government Size, Composition, Volatility and Economic Growth
This paper analyses the effects in terms of size and volatility of government revenue and spending on growth in OECD and EU countries. The results of the paper suggest that both variables are detrimental to growth. In particular, looking more closely at the effect of each component of government revenue and spending, the results point out that i) indirect taxes (size and volatility); ii) social contributions (size and volatility); iii) government consumption (size and volatility); iv) subsidies (size); and v) government investment (volatility) have a sizeable, negative and statistically significant effect on growth.
14486377
A Sensitivity Analysis of Cross-Country Growth Regressions
A vast amount of literature uses cross-country regressions to find empirical links between policy indicators and long-run average growth rates. The authors study whether the conclusions from existing studies are robust or fragile when small changes in the list of independent variables occur. They find that although"policy"appears to be importantly related to growth, there is no strong independent relationship between growth and almost every existing policy indicator. They also find that very few macroeconomic variables are robustly correlated with cross-country growth rates. They clarify the conditions under which one finds convergence of per capita output levels and confirm the positive correlation between the share of investment in GDP and long-run growth. They conclude that all findings using the share of exports in GDP could be obtained almost identically using the total trade or import share and also that few commonly used fiscal indicators are robustly correlated with growth. Finally, the authors highlight the importance of considering alternative specifications in cross-country growth regressions.
14765295
Growth Determinants Revisited
This paper revisits the cross-country growth empirics debate using a novel Limited Information Bayesian Model Averaging framework to address model uncertainty in the context of a dynamic growth model in panel data with endogenous regressors. Our empirical findings suggest that once model uncertainty is accounted for there is strong evidence that initial income, investment, life expectancy, and population growth are robustly correlated with economic growth. We also find evidence that debt, openness, and inflation are robust growth determinants. Overall, the set of our robust growth determinants differs from those identified by other studies that incorporate model uncertainty, but ignore dynamics and/or endogeneity. This underscores the importance of accounting for model uncertainty and endogeneity in the investigation of growth determinants.
153455866
Output volatility and economic growth
This paper proposes a new instrument to identify the causal effect of output volatility on economic growth, which is based on (exogenous) volatility spillovers from abroad. Cross-section evidence from 128 countries points to a negative effect of volatility on growth.
153935803
The Fischer Black Hypothesis: Some Time-Series Evidence
We estimate an ARCH-M model to analyze the relationship between the conditional standard deviation of real gross national product (GNP) and its growth rate for the period 1871-1993. We find that variability significantly increases output growth rates. In addition, impulse response functions show that the effect of variability on growth rates is dynamic. These results provide evidence in favor of Black's (1987) business cycle hypothesis.
154973338
Business cycles in a two-sector model of endogenous growth
Summary. This paper analyzes the impact of cyclical volatility on long-term economic growth: does growth increase or decrease with increased cyclical volatility? We construct a stochastic two-sector model of endogenous growth to analyze this question in detail. We will show that economic growth is higher in the presence of business cycles, since people devote more time to learning activities in an uncertain economic environment. Human capital is a hedge against future income uncertainty. Hence, the rate of economic growth will be higher in a stochastic environment. Based on a calibration of the model, we find that economic growth increases by 0.46%-point as a result of observed business cycle variability. When account is taken of the interaction between the model's general equilibrium and the cycle, welfare gains (measured in units of a permanent percentage increase in consumption) from eliminating business cycle volatility are approximately 1.87%.
155029998
Uncertainty-driven growth
In this paper, I present a model in which firm-level uncertainty raises aggregate productivity growth. The mechanism for this is learning-by-doing in the research sector: firms undertake research to reduce uncertainty, which results in social knowledge accumulation that improves the productivity of future research. The model explains the positive correlation between TFP growth and dispersion in manufacturing industries.
157969780
Growth and Volatility
Growth and volatility correlate negatively across countries, but positively across sectors. Analytically, whether or not sectoral growth and volatility are correlated positively is irrelevant in the aggregate. Cross-country estimates identify the detrimental effects of macroeconomic volatility on growth, but they cannot be used to dismiss theories implying a positive growth-volatility coefficient, which appear to hold in sectoral data. In particular, volatile sectors command high investment rates, as they would in a mean-variance framework.
13821758
Volatility and growth: Credit constraints and the composition of investment
How does uncertainty and credit constraints affect the cyclical composition of investment and thereby volatility and growth? This paper addresses this question within a model where firms engage in two types of investment: a short-term one; and a long-term one, which contributes more to productivity growth. Because it takes longer to complete, long-term investment has a relatively less cyclical return; but it also has a higher liquidity risk. The first effect ensures that the share of long-term investment to total investment is countercyclical when financial markets are perfect; the second implies that this share may turn procyclical when firms face tight credit constraints. A novel propagation mechanism thus emerges: through its effect on the cyclical composition of investment, tighter credit can lead to both higher volatility and lower mean growth. Evidence from a panel of countries provides support for the model's key predictions.
154962285
Long-Term Growth and Short-Term Economic Instability
When learning-by-doing is at the origin of growth, we show that growth rates should be negatively related to the amplitude of the business cycle if the growth rate in human capital is increasing and concave in the cyclical component of production. Empirical evidence strongly supports this finding for industrialized countries and European regions. Using the standard control variables, we find that countries and regions that have higher standard deviations of growth and of unemployment have lower growth rates. The result does not come from an effect of instability on investment. The negative relation does not hold for non-industrialized countries, however, for which learning-by-doing may not to be the main engine of growth.
15414622
The New Growth Evidence
Why do growth rates differ? This paper surveys the recent empirical literature on economic growth, starting with a discussion of stylized facts, data problems, and statistical methods. Six research questions are emphasized, drawing on growth and convergence research. In answering these questions, the paper argues that efficiency has grown at different rates across countries, casting doubt on neoclassical models in which technology is a public good. The latter half of the paper rounds up a variety of findings before providing answers to all six questions, including a short summary of how differences in growth rates arise.
845683
On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations
This paper studies how the Hodrick-Prescott filter should be adjusted when changing the frequency of observations. It complements the results of Baxter and King (1999) with an analytical analysis, demonstrating that the filter parameter should be adjusted by multiplying it with the fourth power of the observation frequency ratios. This yields an HP parameter value of 6.25 for annual data given a value of 1600 for quarterly data. The relevance of the suggestion is illustrated empirically.
620090
Business Cycle Volatility and Economic Growth: A Reassessment
One of the important implications of real business cycle theory is that there should be a positive relationship between economic fluctuations and economic growth, or, to be more specific, that the growth of real gross domestic product per capita should fall as the business cycle becomes less volatile. This is, of course, a conjecture that is open to empirical verification, at least in principle, but there are a variety of approaches that may be taken that will not necessarily yield consistent sets of findings. Altman (1995), for example, uses primarily the Maddison (1991) data set of some 13 countries from 1870 to 1986 and detrends using log-linear trend lines across benchmark years to obtain the cyclical component of output. He then uses rank and linear correlation techniques to assess the strength of a possible positive relationship between cyclical volatility-measured as the standard deviation of the cyclical component-and output growth across a variety of subperiods. Altman finds little evidence in favor of this implication of real business cycle models, but it may be argued that his conclusion relies heavily on two features of his empirical approach: the method used to construct the cyclical components and the correlation techniques employed to assess the strength of any relationship between cyclical volatility and growth. The aim of the present paper is to assess the robustness of this evidence by extending Altman's analysis in three directions. The first is to use a more extensive output per capita data set-we employ Maddison's (1995) updated set of22 countries, which now ends in 1994. We then employ several statistical techniques that are explicitly designed to extract business cycle components from annual economic time series and, finally, we use robust nonparametric methods to investigate the relationship between cyclical volatility and growth.
32743542
International evidence on the historical properties of business cycles
We document properties of business cycles in ten countries over the last hundred years, contrasting the behavior of real quantities with that of the price level and the stock of money. Although the magnitude of output fluctuations has varied across countries and periods, relations among variables have been remarkably uniform. Consumption has generally been about as variable as output, and investment substantially more variable, and both have been strongly procyclical. The trade balance has generally been countercyclical. The exception to this regularity is government purchases, which exhibit no systematic cyclical tendency. With respect to the size of output fluctuations, standard deviations are largest between the two world wars. In some countries (notably Australia and Canada) they are substantially larger prior to World War I than after World War II, but in others (notably Japan and the United Kingdom) there is little difference between these periods. Properties of price levels, in contrast, exhibit striking differences between periods. Inflation rates are more persistent after World War II than before, and price level fluctuations are typically procyclical before World War II, countercyclical afterward. We find no general tendency toward increased persistence in money growth rates, but find that fluctuations in money are less highly correlated with output in the postwar period.
123204039
Estimation and inference in econometrics
Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.
153011143
The Curious Attraction of Wagner's Law
Wagner's ‘law of increasing state activity’ has recently been subjected to intensive use of recondite econometric testing procedures. An examination of the relevant articles reveals ignorance both of Wagner's definition of ‘state activity’ and of his insistence that he was not engaged in prediction. Consequently, the omission of public enterprises contained in Wagner's definition leads to a model misspecification and the object of testing his hypothesiss remains obscure.
3136786
The size and composition of government expenditure
This paper tests several leading hypotheses on determinants of government expenditure. The purpose is to avoid omitted variables bias by testing the prominent theories in a comprehensive specification, to identify persistent puzzles for the current set of theories, and to explore those puzzles in greater depth by looking at the composition of government expenditure and the level of government at which it takes place as well as its magnitude. Using Global Financial Statistics data from the IMF covering over 100 countries from 1970-2000, I look at cross-sectional and inter-temporal variation in government expenditure and both individual categories of expenditure (such as defense, education, health care) and different levels of government (central, state, and local). Among other results, I find a new explanation for Wagner's Law, widespread evidence that preference heterogeneity leads to decentralization rather than outright decreases in expenditures, that a great deal of the expenditure associated with increased trade openness is not in categories that explicitly insure for risk, and evidence that both political access and income inequality affect the extent of social insurance.
15447313
Institutional Causes, Macroeconomic Symptoms: Volatility, Crises and Growth
Countries that have pursued distortionary macroeconomic policies, including high inflation, large budget deficits and misaligned exchange rates, appear to have suffered more macroeconomic volatility and also grown more slowly during the postwar period. Does this reflect the causal effect of these macroeconomic policies on economic outcomes? One reason to suspect that the answer may be no is that countries pursuing poor macroeconomic policies also have weak 'institutions,' including political institutions that do not constrain politicians and political elites, ineffective enforcement of property rights for investors, widespread corruption, and a high degree of political instability. This paper documents that countries that inherited more 'extractive' instit utions from their colonial past were more likely to experience high volatility a nd economic crises during the postwar period. More specifically, societies where European colonists faced high mortality rates more than 100 years ago are much more volatile and prone to crises. Based on our previous work, we interpret this relationship as due to the causal effect of institutions on economic outcomes: Europeans did not settle and were more likely to set up extractive institutions in areas where they faced high mortality. Once we control for the effect of institutions, macroeconomic policies appear to have only a minor impact on volatility and crises. This suggests that distortionary macroeconomic policies are more likely to be symptoms of underlying institutional problems rather than the main causes of economic volatility, and also that the effects of institutional differences on volatility do not appear to be primarily mediated by any of the standard macroeconomic variables. Instead, it appears that weak institutions cause volatility through a number of microeconomic, as well as macroeconomic, channels.
154180405
Political institutions and economic volatility
We examine the effect of political 'institutions' on economic growth volatility, using data from more than 100 countries over the period 1960 to 2005, taking into account various control variables as suggested in previous studies. Our indicator of volatility is the relative standard deviation of the growth rate of GDP per capita. The results of a dynamic panel model indicate that democracy reduces economic volatility. We also find that some dimensions of political instability and policy uncertainty increase economic volatility.
17294815
Why is GDP growth so much more volatile in poor countries than in rich ones ?
Why is GDP growth so much more volatile in poor countries than in rich ones? We identify four possible reasons: (i) poor countries specialize in more volatile sectors; (ii) poor countries specialize in fewer sectors; (iii) poor countries experience more frequent and more severe aggregate shocks (e.g. from macroeconomic policy); and (iv) poor countries' macroeconomic fluctuations are more highly correlated with the shocks of the sectors they specialize in. We show how to decompose volatility into these four sources, quantify their contribution to aggregate volatility, and study how they relate to the stage of development. We document the following regularities. First, as countries develop, their productive structure moves from more volatile to less volatile sectors. Second, the level of specialization declines with development at early stages, and slowly increases at later stages of development. Third, the volatility of country-specific macroeconomic shocks falls with development. Fourth, the covariance between sector-specific and country-specific shocks does not vary systematically with the level of development. We argue that many theories linking volatility and development are not consistent with these findings and suggest new directions for future theoretical work.
16989050
Openness, Country Size and the Government
This paper shows that smaller countries have a larger share of public consumption in GDP, and are also more open to trade. These empirical observations are consistent with recent theoretical models explaining country formation and break up, and may account for the observed positive empirical relationship between trade openness and government size.
53383615
How Accurate are Real-Time Estimates of Output Trends and Gaps?
Real-time estimates of output gaps and trends are important tools for macroeconomic analysis. But how accurate are estimates of real-time gaps and trends? This article discusses the problem of estimating gaps and trends in real time and constructs measures of their precision. The analysis is based on band-pass filtering methods augmented with univariate forecasts. The empirical analysis suggests that there is considerable uncertainty associated with real-time estimates of trends and gaps.
57567299
Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series
Band-pass filters are useful in a wide range of economic contexts. This paper develops a set of approximate band-pass filters and illustrates their application to measuring the business-cycle component of macroeconomic activity. Detailed comparisons are made with several alternative filters commonly used for extracting business-cycle components.