Ray Fair applies his macroeconometric model to study the central features of the U.S. macroeconomy such as price stability and full employment in the dual mandate.

Charlene Vos

2021-09-07 09:31:00 Tue ET

Ray Fair applies his macroeconometric model to study the central features of the U.S. macroeconomy such as price stability and full employment in the dual mandate.

Ray Fair (2004)


Estimating how the macroeconomy works


Yale macroeconomic empiricist Ray Fair builds, estimates, and applies his macro model to study the central features of the U.S. economy. This practical application helps analyze many important empirical macro questions, such as whether the U.S. economy has structurally changed from a new age of high productivity in the 1990s to the low-interest-rate and low-growth macro environment with price stability and maximum sustainable employment in the Federal Reserve dual mandate. Several economists can place this work in the broader context of the historical evolution of aggregate econometric methods. This focus compares and contrasts with the new developments in both the estimation and calibration of dynamic stochastic general equilibrium (DSGE) macro models. With a multi-country macroeconometric model, Fair delves into several important empirical questions. These empirical questions include the root causes of inflation, monetary policy decisions, macro stabilization limits and constraints, the wealth and income ripple effects on macro consumption, the comparisons of American, British, and European monetary policy restrictions, and the macro stabilization costs of ubiquitous Euro currency conversion in Europe. Fair empirically finds little evidence in support of the rational expectations evolution and the non-accelerating inflation rate of unemployment (NAIRU). We can thereby apply this empirical result to better demystify the puzzle that there is a mysterious and inexorable trade-off between inflation and unemployment. In this new light, we need to consider the monetary policy goals and performance metrics for the central bank in the broader context of both fiscal-monetary policy coordination and macro financial asset market stabilization.


The new classical rational expectations revolution has structurally transformed the FRB-MIT-Penn ARIMA model representation of the U.S. economy to the Kydland-Prescott real business cycle (RBC) macro model with dynamic stochastic general equilibrium (DSGE) calibration and estimation.

Nobel Laureate Christopher Sims (1980) pioneers the use and estimation of vector autoregressions (VAR) as robust flexible time-series summaries and descriptions of macroeconometric dynamism. Vector autoregression evidence shows that most interest rate increases help dampen economic output growth and employment with 6-month to 1-year lags. Also, this evidence further suggests that interest rate hikes help dampen inflation with 1-year to 2-year lags. This macro legacy demonstrates that monetary policymakers should follow Taylor interest rate rules in response to inflation, asset market stabilization, and the output gap. The salient empirical facts from post-war data match quite well the U.S. macroeconomy and reality.

Together Nobel Laureates Christopher Sims and Thomas Sargent analyze rational expectations in several macroeconometric models in this rare and unique fashion. Christopher Sims and Thomas Sargent (1977) propose the use of structural vector autoregressions (SVAR) in business cycle analysis with prior theoretic restrictions. This research shows that transient monetary policy shocks can drive real economic output and inflation outcomes. Subsequent research establishes several economic time-series facts. First, it would be best to view monetary policy as an interest rate rule. The standard interest rate rule often leads to welfare loss minimization in both stochastic calibration and empirical estimation. Second, most variation in monetary policy instruments (such as interest rates and inter-bank reserves) comprises new systematic reactions to asset fluctuations in the general state of the U.S. economy. Random monetary disturbances, however, explain little of business cycle variation. Third, real GDP economic output responds to interest rate changes with a lag, and price inflation reacts to interest rate changes with an even longer lag. These macro features prevail in both the U.S. and many other countries with sound and efficient financial development.

Nobel Laureates Finn Kydland and Edward Prescott launch and then pioneer the real business cycle of macroeconomic reality in America and most OECD countries. The real business cycle (RBC) theory proves to be a watershed event for modern macroeconomics. Kydland and Prescott (1982) add persistent technology shocks to a dynamic stochastic general equilibrium (DSGE) version of the optimal growth model due to Brock and Mirman (1972). Data discipline comes through calibration, which serves as a new methodology of soft hypothesis test evidence. This method avoids the trouble of estimating large structural models (e.g. the Klein-Goldberger structural core model comprises 15 equations and 5 identities). Simple and intuitive calibration typically uses parameter values for consumer tastes, firm preferences, endowments, and technological advances drawn from microeconomic data, panel observations, industry empirics, and so forth. Kydland and Prescott (1982) can add highly persistent exogenous shocks to total factor productivity (TFP). The artificial model generates imaginary macroeconomic time series on real GDP and its major components, labor supply, capital investment, and other endogenous variables of interest. Kydland and Prescott (1982) find that their model matches pretty well the dispersion of U.S. macroeconomic time series (except for one small fundamental flaw that labor supply fluctuates much more than wage growth in the data).

The RBC macro model explains several salient features of the post-war economy. First, economic boom-bust fluctuations exhibit no regular cyclical pattern. At more or less random intervals, many exogenous disturbances of various types and sizes perturb the economy. These random disturbances would then propagate through the economy. Second, the major components of output show uneven distributions of boom-bust fluctuations. Although inventory investment on average accounts for only a small fraction of U.S. GDP, capital inventory fluctuations account for almost half of U.S. GDP in recessions relative to normal booms. Consumer purchases of durable goods and residential and non-residential business investments account for almost the other half of U.S. GDP. Third, U.S. GDP exhibits some asymmetry in time-series movements. American output seems to be above its usual trend path over relatively long time horizons with brief periods when U.S. output retrenchment persists below its typical trend path. Fourth, the U.S. economy enjoys remarkable macrofinancial stability during the Great Moderation from the early-1980s to 2020. This expansionary episode represents the longest boom in U.S. economic history. During this specific period, the natural rate of interest has fallen substantially with low and stable inflation. The Global Financial Crisis 2008-2009 represents a sharp change from the macroeconomic stability of recent decades. However, one severe long recession is not enough for most macroeconomists to bring average volatility back to its long-run average in the early post-war decades. The global corona virus crisis of 2020-2021 represents a severe but brief recession as the global economy gradually returns to the new normal steady state. It is probably too soon to know whether the recent crises represent the end of the Great Moderation or some one-time aberration. Finally, the conjunction of declines in both productivity gains and labor work hours suggests that changes in the unemployment rate are smaller than changes in U.S. GDP. The Okun law shows the robust relation between changes in U.S. GDP and the unemployment rate. In particular, a 3% shortfall in U.S. GDP relative to normal growth often produces a 1%-point increase in the unemployment rate. Overall, the RBC macro model calibration matches well these salient features of the post-war economy in America, Britain, Canada, Europe, and Japan etc.

Nobel Laureate Robert Lucas (1976) offers his famous critique of a lack of explicit microfoundations of the large-scale classic Keynesian macroeconometric models. These large-scale Keynesian models not only disconnect from standard economic intuition, but also imply that the macroeconometric systems would not be adequate for policy analysis and evaluation. Economic relations that most economists gauge under one policy regime would not be invariant to structural changes in the regime. For instance, the U.S. economy may not follow the same Taylor interest rate rules if the central bank structurally changes the main policy goal from an inflation target to the dual mandate of both price stability and maximum sustainable employment. The same Lucas critique further applies to the probable scenario where the policy regime changes again from the dual mandate to better address some other goals and concerns such as bank capital regulation, sustainable economic development, and macro financial asset market stabilization etc. Another good example emerges from the context of optimal net income taxation by Nobel Laureate James Mirrlees. Higher levels of income taxes on the rich create fiscal revenue that the government can use to redistribute to the poor through the social transfer system. This Pareto optimal redistribution can often help enhance overall social welfare. However, this income taxation reduces the incentive for the rich to work due to a decrease in the marginal utility of income. As a result, overall labor supply tends to decrease below the Pareto optimal level. These dynamic macro adjustments suggest that most of the incentive constraints on labor supply can offset the additional tax revenue from higher income tax rates. On balance, the Lucas critique offers these key prescient economic insights into the potential net result of both interdependent policy regime changes and behavioral responses.


Fair takes a more skeptical view of modern DSGE macro models in terms of their ability to produce profound fiscal and monetary policy implications for the economy.

Yale macroeconometric professor Ray Fair takes a more skeptical view of modern DSGE macro models. Fair applies the traditional Cowles Commission approach to macroeconometric estimation. Specifically, the Fair multi-country model comprises the U.S. economy and the remainder of the world. The U.S. economy has 6 sectors: households, firms, financial institutions, foreign, federal, and state governments. A joint set of 30 stochastic equations can capture their behaviors and interactions (9 for households, 12 for firms, 5 for financial institutions, 1 for trade imbalances, and 3 for foreign, federal, and state governments). As a result, there are more than 100 economic identities. This Fair multi-country model seems to be more complex than the canonical RBC macro model, but less complex than the large-scale Keynesian macro model of the IS-LM classic economy.

Fair connects the dots between the U.S. economy and the rest of the world through a common set of equations. These equations help pin down trade shares and world prices. When we put together the U.S. and non-U.S. sections of the multi-country macro model, we get 362 stochastic equations, 1,646 coefficients, and 1,111 trade share equations. Fair applies the basic 2-stage least squares (2SLS) regressions to the U.S. and non-U.S. data from 1954 to 2002. Fair carries out a long battery of tests for additional variables, time trends, residual error autocorrelations, lead-lag relations, and forecast efficiency gains and losses etc.

Fair follows the neoclassical Keynesian tradition to specify several core equations. For instance, consumption depends upon wealth, income, and the interest rate (for intertemporal substitution across time horizons). Capital investment accumulation depends on economic output and the interest rate. Prices and wages follow some changes in labor productivity, import and export prices, unemployment rates, and prior prices and wages. Besides, the Fair multi-country macro model accounts for all balance-sheet and flow-of-funds constraints as well as demographic structures. Drawing data from several government agencies such as the National Income and Product Accounts (NIPA) and the Bureau of Economic Analysis (BEA), Fair helps estimate the multi-country macro model with some remarkable policy prescriptions. Specifically, there is no or little evidence in support of rational expectations. As a result, monetary policy decisions and interest rate adjustments often lead to robust persistent non-neutral ripple effects on economic boom-bust fluctuations over time. Moreover, Fair reports no or little evidence of the non-accelerating inflation rate of unemployment (NAIRU), but the negative results cannot preclude the existence of a neutral interest rate. In summary, this neutral interest rate represents the short-term real interest rate that the central bank targets to boost economic output back to full employment with low and stable inflation. Nowadays, many monetary policy-makers apply and estimate the neutral interest rate to help attain price stability and maximum employment in the dual mandate worldwide.

Fair further delves into the empirical questions such as the root causes of inflation, monetary policy decisions, macro stabilization limits, the wealth and income ripple effects on consumption, the key comparisons of American and European monetary policy restrictions, and the stabilization costs of Euro currency usage in Europe. In regard to the root causes of inflation, Fair finds that inflation manifests in the form of general price increases as a consequence of either seigniorage taxes or nominal price rigidities. When the fiscal authority uses incessant Treasury bond issuances to fund fiscal deficits on top of public debt burdens, inflationary concerns arise from general price increases sooner or later. Alternatively, nominal price-wage rigidities can turn small menu costs into much higher general price hikes for monopolistically competitive firms to maintain their price markups and profits in due course. These nominal price-wage rigidities persist as disequilibrium general price increases. The net result is higher inflation. Recent empirical studies show that the welfare cost of inflation remains relatively low. A 10% increase in core inflation suggests a broader 0.1% to 0.3% contraction in real GDP economic output. In this fresh light, it is quite reasonable for the central bank to attain better economic growth, full employment, and sustainable development etc with relatively low and stable inflation.

With respect to the wealth and income ripple effects on consumption, Fair reports evidence in support of the multiplier-accelerator model for business cycle analysis. The Keynesian multiplier arises as a natural result of both consumption and capital investment accumulation in response to the intermediate rate of economic growth. There are several solutions for real GDP national income in a second-order linear difference equation. At each point in time, real GDP national income can be shown as a linear combination of its 1-quarter minus 2-quarter lags. The major parameters show the propensity to consume a fraction of real GDP national income, as well as the major pace of capital investment changes in response to changes in aggregate consumption. A high Keynesian multiplier indicates higher economic growth when the government tends to spend more. In accordance with the multiplier-accelerator model, the net positive effect is greater than the total dollar amount of government expenditures. Whether this Keynesian multiplier can sustain in the medium to long run depends on fiscal factors such as optimal taxation and public debt issuance.

Both the U.S. Federal Reserve System and European Central Bank leverage their core monetary policy instruments: short-run interest rate adjustments, quantitative-easing large-scale asset purchases, and bank reserve requirements. Fair finds that the Federal Reserve System tends to focus on near-zero short-term interest rates and large-scale asset purchases in order to improve GDP economic output, capital investment accumulation, and employment. By comparison, the European Central Bank uses a reasonable combination of zero to negative interest rates, large-scale asset purchases, and low bank reserve requirements to provide monetary stimulus. In turn, this monetary stimulus helps enhance economic output, capital investment, and regional employment in Europe. However, the recent Brexit movement shows substantial macro stabilization costs of Euro currency adoption in Europe. In recent decades, the British pound sterling remains the long prevalent currency in England, and the Bank of England continues to operate monetary policy and macrofinancial policy choices and decisions in an independent and cost-effective manner. In other words, the Great Britain enjoys monetary policy independence from Europe. In this fundamental sense, the Fair macroeconometric analysis shows large stabilization costs of Euro currency adoption across England and Europe. In recent years, the European sovereign debt crisis persists as a key perennial macrofinancial problem in Portugal, Italy, Greece, and Spain (PIGS). In this negative light, Europe requires fiscal integration of national treasuries in order to better balance fiscal deficits on top of public debt burdens in several parts of Europe. From a pragmatic viewpoint, France and Germany should lead PIGS and other European countries to assuage these sovereign debt and deficit concerns.


The Fair macroeconometric model estimation deals with both adaptive and rational expectations, both stationary and non-stationary time-series, and microeconomic data foundations.

Fair includes U.S. GDP lags as explanatory variables in many of the equations as part of his macroeconometric multi-country analysis. These U.S. GDP lags turn out to be econometrically significant after Fair controls for autoregressive properties of the Gaussian error term. These lags may capture either any partial adjustments or any adaptive expectations. Fair recognizes the fact that this choice puts him in the minority in the economic profession because rational expectations are often a good approximation of actual behaviors in most macroeconometric time-series analysis. However, Fair argues that most economic actors follow their simple intuition to find consistent adaptive expectations over time. This model choice specifies the role of heterogeneity of beliefs in the Fair macroeconometric model. This case somehow resembles the long prevalent evidence in macrofinance that the marginal investor determines the stochastic discount factor for asset return prediction in equilibrium. With heterogeneous beliefs, both adaptive and rational expectations can often help determine the equilibrium stochastic discount factor in the cross-section of average asset returns.

With a macroeconometric multi-country model, Fair has to deal with both stationary and non-stationary economic time-series. This macroeconometric estimation does not affect the point estimates and standard errors. Also, bootstrap simulation often helps correct the asymptotic approximation in the non-stationary case. On balance, the Fair macroeconometric estimation rests on the core hypothesis that economic covariates are stationary around their respective deterministic trends. Fair further acknowledges the empirical fact that more complex specifications (such as fractal integration and long memory model design etc) are likely to better characterize the post-war U.S. macroeconomic time-series data.

Fair further recognizes the empirical fact of structural breaks in the late-1970s and the mid-1990s. These structural breaks indicate changes in the basic structure of the U.S. macroeconomy. Exogenous oil shocks and neutral interest rate decreases both serve as structural breaks in the Fair macroeconometric estimation. There is considerable evidence of parameter drifts when Fair estimates his macroeconomic multi-country model. Another possibility behind parameter changes over time may be the presence of stochastic volatility. Many macro economists refer to the large decline in observable volatility of macroeconomic aggregates (such as U.S. GDP) as the Great Moderation from the mid-1990s to at least 2020. It is too soon to know whether the recent corona virus crisis represents the end of the Great Moderation or some one-time aberration.

Fair finds that his macroeconometric multi-country model performs better than the 7-variable vector autoregression (VAR). With respect to non-stationary economic time-series, Fair proposes the use of cointegration in some vector error correction model (VECM). Cointegration arises from the case where multiple macroeconomic time-series co-move together so that some linear combination of these time-series turns out to be stationary in the standard econometric sense. The long-run macro restrictions can help control econometric behaviors and forecast capabilities in the medium term. Overall, all these empirical developments help us better understand the core macroeconomic threads and insights in both teleological and nomological ways.


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