Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach

To verify that the New Neoclassical Synthesis model can explain the main features of US macro data, to test which of its many frictions are empirically necessary, and to use it on a set of business cycle questions (Non-technical summary, ECB Working Paper 722, pp. 5-6). “As the NNS models have become the standard workhorse for monetary policy analysis, it is important to verify whether they can explain the main features of the US macro data.” On frictions: “the introduction of a large number of frictions raises the question whether each of those frictions are really necessary to describe the seven data series. The Bayesian estimation methodology provides a natural framework for testing which frictions are empirically important by comparing the marginal likelihood of the various models.” The applications concern the driving forces of output, the output-inflation cross correlation, the employment effect of productivity shocks, and the sources of the Great Moderation.

Sticky Calvo prices and wages with backward indexation, habit formation, investment adjustment costs, variable capital utilisation and fixed costs, estimated on 1966:1-2004:4 (Non-technical summary, p. 5, and Section 3, p. 17 fn. 7). The frictions “create hump-shaped responses of aggregate demand.” On the sample: “The data set used generally starts in 1947. However, in previous versions of this paper we found that the first ten years are not representative of the rest of the sample, so that we decided to shorten the sample to 1957:1 - 2004:4. In addition, below in Section 4 we use the first 10 years as a training sample for calculating the marginal likelihood of unconstrained VARs, so that the effective sample starts in 1966:1.”

Five: two because they would be hard to estimate without additional measurement equations, three because they are not identified (Section 3.1, p. 18). Quarterly depreciation is fixed at 0.025 and the exogenous spending-GDP ratio at 18 percent – “Both of these parameters would be difficult to estimate unless the investment and exogenous spending ratios would be directly used in the measurement equation.” The steady-state labour market mark-up is set at 1.5 and the curvature parameters of the Kimball aggregators in the goods and labour markets are both set at 10, these three being “clearly not identified.”

Deliberately harmonised and fairly standard, with a reported robustness check (Section 3.1, pp. 18-19). Innovation standard errors follow inverse-gamma distributions with mean 0.10 and two degrees of freedom, “a rather loose prior”; AR(1) persistences are beta with mean 0.5 and standard deviation 0.2. The policy rule priors follow a standard Taylor rule – long-run inflation and output-gap responses normal around 1.5 and 0.125 (0.5 divided by 4), lagged interest rate coefficient normal around 0.75. The intertemporal elasticity of substitution is centred at 1.5, habit at 0.7, labour supply elasticity at 2; the investment adjustment cost parameter at 4 following Christiano, Eichenbaum and Evans; the Calvo probabilities at 0.5 for both prices and wages, “suggesting an average length of price and wage contracts of half a year … compatible with the findings of Bils and Klenow (2004) for prices,” with indexation priors also at 0.5. A footnote reports that increasing the prior standard errors of the behavioural parameters by 50 percent leaves the results “very similar,” and a later footnote adds that “when relaxing the prior distributions, it turns out that the degree of wage stickiness rise even more, whereas the degree of price indexation falls by more.”

Price and wage stickiness are higher, price indexation much lower, investment adjustment costs higher, fixed costs much higher and the capital share much lower (Section 3.2, pp. 19-20, Table 1). “The average duration of wage contracts is somewhat less than a year; whereas the average duration of price contracts is about 3 quarters. The mean of the degree of price indexation (0.24) is on the other hand estimated to be much less then 0.5.” The fixed cost parameter is estimated at 1.6 against a prior mean of 0.25, and the capital share at 0.19. The data are described as “quite informative on the behavioural parameters as indicated by the lower variance of the posterior distribution relative to the prior distribution,” with two exceptions where “the posterior and prior distributions are quite similar”: the elasticity of labour supply and the elasticity of the cost of changing capital utilisation. Trend growth is estimated at about 0.43 quarterly, steady-state inflation at about 3 percent annually, and implied steady-state nominal and real rates at about 6 and 3 percent.

A high long-run inflation response, considerable smoothing, a weak response to the output gap level and a stronger response to its change (Section 3.2, p. 20). “The mean of the long-run reaction coefficient to inflation is estimated to be relatively high (2.0). There is a considerable degree of interest rate smoothing as the mean of the coefficient on the lagged interest rate is estimated to be 0.81. Policy does not appear to react very strongly to the output gap level (0.09), but does respond strongly to changes in the output-gap (0.22) in the short run.”

Marginal likelihood against VARs and a Sims-Zha BVAR with a training sample, plus a rolling RMSE exercise; the model matches the best BVAR at one quarter and beats it at longer horizons (Section 4, pp. 20-22, Tables 2-3). Following Sims, “it is important to use a training sample in order to standardize the prior distribution across widely different models,” so 1956:1-1965:4 serves that role. “The tightly parameterized DSGE model performs much better than an unconstrained VAR in the same vector of observable variables,” with the unconstrained VAR’s marginal likelihood deteriorating quickly as lag order rises. The Sims-Zha BVAR – combining a Minnesota-type prior with priors on persistence and cointegration, with real GDP, consumption, investment and the real wage in log levels – does much better, and “the best BVAR model (BVAR(4)) does as well as the DSGE model.” The authors’ summary is appropriately narrow: “the estimated DSGE model can compete with standard BVAR models in terms of empirical one-step-ahead prediction performance.” The RMSE exercise estimates VAR(1), BVAR(4) and the DSGE model over 1966:1-1989:4 and forecasts 1990:1-2004:4, re-estimating the VARs every quarter and the DSGE model every year, with overall performance measured by the log determinant of the uncentered forecast error covariance matrix. “At the one-quarter ahead horizon, the BVAR(4) and the DSGE model improve with about the same magnitude over the VAR(1) model … However, over longer horizons up to three years, the DSGE model does considerably better than both the VAR(1) and BVAR(4) model.”

Price and wage stickiness and investment adjustment costs; indexation and variable capital utilisation do not (Section 5, pp. 22-24, Table 4). “Reducing the degree of nominal price and wage stickiness to a Calvo probability of 0.10 is about equally costly in terms of a deterioration of the marginal likelihood. In both cases the marginal likelihood falls very significantly by about 50.” The compensating adjustments are informative: cutting price stickiness pushes estimated price indexation from 0.22 to 0.84 and raises the variance and persistence of price mark-up shocks; cutting wage stickiness drops the estimated labour supply elasticity from 1.92 to 0.25, and “in terms of short run dynamics, these changes more or less cancel out.” On indexation: “restricting the price indexation parameter to a very low value of 0.01 leads to an improvement of the marginal likelihood, suggesting that empirically it would be better to leave this friction out.” On the real side, removing investment adjustment costs costs about 160 in marginal likelihood – the largest single effect; reducing habit is “quite costly, although much less so”; “the presence of variable capital utilisation does not seem to matter for the model’s performance. Shutting this off comes at no cost”; but reducing the share of fixed costs in production to 10 percent is costly. The authors also note a contrast with the literature: “Contrary to the discussion in King and Rebelo (2000), the absence of variable capital utilisation does not increase the standard error of the productivity shock in our model.”

Demand-type shocks in the short run, supply-type shocks beyond two years, and monetary policy shocks almost nowhere (Section 6.1, pp. 24-25, Figures 1-4). Exogenous spending, risk premium and investment-specific technology shocks “account for more than 50 percent of the forecast error variance of output up to one year,” each classifiable as a demand shock “in the sense that they have a positive effect on output, hours worked, inflation and the nominal interest rate under the estimated policy rule.” But “in line with the results of Shapiro and Watson (1989), it is mostly two ‘supply’ shocks, the productivity and the wage mark-up shock, that account for most of the output variations in the medium to long run. Indeed, even at the two year horizon, together the two shocks account for more than 50% of the variations in output.” A typical positive wage mark-up shock “gradually reduces output and hours worked by 0.8 and 0.6 percent respectively.” On monetary policy: “Confirming the large identified VAR literature on the role of monetary policy shocks … monetary policy shocks contribute only a small fraction of the forecast variance of output at all horizons.” Historically, the recessions of the early 1990s and the early 2000s are attributed mainly to demand shocks, the 1974 recession mainly to positive mark-up shocks associated with the oil crisis, and only the early 1980s recession to monetary policy shocks under Volcker.

Price and wage mark-ups at all horizons, for two stated reasons: a flat Phillips curve and an aggressive estimated policy rule (Section 6.2, pp. 25-26). “At all horizons, price and wage mark-ups are the most important drivers of inflation. In the short run, price mark-ups dominate, whereas in the medium to long run wage mark-ups become relatively more important.” The explanation is given explicitly: “First, the estimated slope of the New Keynesian Phillips curve is very small, so that only large and persistent changes in the marginal cost will have an impact on inflation. Second, and more importantly, under the estimated monetary policy reaction function the Fed responds quite aggressively to emerging output gaps and their impact on inflation” – reflected in the fact that at short and medium horizons “more than 60 percent of variations in the nominal interest rate are due to the various demand and productivity shocks.” Historically, mark-up shocks are the dominant source of secular inflation shifts, “however, also monetary policy did play a role in the rise of inflation in the 1970s and the subsequent disinflation during the Volker period.”

Yes, and the correlations it generates are significantly different from zero (Section 6.2, pp. 26-27, Figure 5). The empirical correlation function of HP-detrended output and inflation over 1966:1-2004:4 is compared against the median and 5-95 percent bands generated from 1,000 posterior draws simulating samples of the same length. “Figure 5 clearly shows that the DSGE model is able to replicate both the negative correlation between inflation one to two years in the past and current output and the positive correlation between current output and inflation one year ahead.” Decomposing the cross-covariance, “the negative correlation between current inflation and future output is mostly driven by the price and wage mark-up shocks. In contrast, the positive correlation between the current output gap and future inflation is the result of both demand shocks and mark-up shocks.” Monetary policy shocks play no role both because they explain little of inflation and output and because “the peak effect of a policy shock on inflation occurs before its peak effect on output.”

Hours fall immediately and significantly, turning positive only after two years – and this happens under flexible prices too, so it is not a nominal-rigidity result (Section 6.3, pp. 27-28, Figure 7). Against the debate between Galí, Francis and Ramey, and Galí and Rabanal on one side and Christiano et al., Dedola and Neri, and Peersman and Straub on the other, “Overall, the estimates confirm the analysis of Gali (1999) and Francis and Ramey (2004).” At business cycle frequencies productivity shocks account for about 25 to 30 percent of the forecast error variance of output. “Moreover, our estimation results show that it is mainly the estimated degree of habit persistence and the importance of capital adjustment costs that explain the negative impact of productivity on hours worked … Indeed, also under flexible prices, hours worked would fall significantly,” from which the authors draw a policy conclusion: “Given these estimates, it is unlikely that a more accommodative monetary policy would lead to positive employment effects.” Two reasons are offered for the weak medium-run positive effect: the shock, though persistent, is temporary, so output is already returning to baseline when the hours effects materialise; and a positive productivity shock reduces fixed cost per unit of production, so less labour is required for a given output.

Structural parameters largely stable; shock variances, the output-gap policy response, stickiness and indexation the exceptions (Section 6.4, pp. 28-29, Table 5). Comparing 1966:2-1979:2 with 1984:1-2004:4, “the most significant differences between the two sub-periods concern the variances of the stochastic processes. In particular the standard errors of the productivity, monetary policy and price mark-up shocks (and to a lesser extent the investment shock) seem to have fallen.” Steady-state inflation is only marginally lower (2.6 versus 2.9). “What is different is the central bank’s reaction coefficient to the output gap, which is halved and is no longer significant in the second period. In contrast, the response to inflation is only marginally higher in the second period and the response to the change in the output gap is the same.” The authors place this finding between two literatures: consistent with Orphanides, who finds the relative response to output is what changed, but “at odds with the results of Boivin and Giannoni (2006), which finds that a stronger central bank response to inflation in the second subperiod can account for a smaller output response to monetary policy shocks estimated in identified VARs. In our case, the lower response to the output gap actually increases the output response of a monetary policy shock in the second period.” Price and wage stickiness rise and indexation falls in the second period – consistent with Galí and Gertler’s single-equation sub-sample estimates, and with “the story that low and stable inflation may reduce the cost of not adjusting prices and therefore lengthen the average price duration leading to a flatter Phillips curve.”

Milder shocks, not better policy and not structural change (Section 6.4, pp. 29-30, Table 6). The exercise asks what output growth and inflation volatility would have been in the recent period under 1970s shocks, under the pre-1979 policy rule, or with unchanged structural parameters. “It turns out that the most important drivers behind the reduction in volatility are the shocks, which appear to have been more benign in the last period. A reversal to the monetary policy reaction function of the 1970s would have contributed to somewhat higher inflation volatility and lower output growth volatility, but these effects are very small compared to the overall reduction in volatility. Finally, also the changes in the structural parameters do not appear to have contributed to a major change in the volatility of the economy.” The authors note the model captures the reduction in volatility “although it overestimates the standard deviation somewhat in both periods,” align the result with Stock and Watson and with Sims and Zha, and leave the obvious question open: “It remains an interesting research question whether policy has contributed to the reduction of those shocks.”

That the model class fits the data well conditional on a rich enough stochastic structure, while stressing that the model remains stylised and not yet secure enough for welfare analysis (Section 7, p. 30). “We have shown that modern micro-founded NNS models are able to fit the main US macro data very well, if one allows for a sufficiently rich stochastic structure and set of frictions … Although the estimated structural model is highly restricted, it is able to compete with standard VAR and BVAR models in out-of-sample forecasting, indicating that the theory embedded in the structural model is helpful in improving the forecasts of the main US macro variables, in particular at business cycle frequencies.” The stated limits are twofold: “a deeper understanding of the various nominal and real frictions that have been introduced would increase the confidence in using this type of models for welfare analysis,” and the analysis “raises questions about the deeper determinants of the various ‘structural’ shocks such as productivity and wage mark-up shocks that are identified as being important driving factors of output and inflation developments.”