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Prepared for the 19th NBER Annual Conference on Macroeconomics. We are thankful to Susanto Basu, Olivier Blanchard, Yongsung Chang, John Fernald, Albert Marcet, Barbara Rossi, Julio Rotemberg, Juan Rubio-Ramirez, Robert Solow, Jaume Ventura, Lutz Weinke, as well as the editors, Mark Gertler and Ken Rogoff, and discussants, Ellen McGrattan and Valerie Ramey, for useful comments. We have also benefited from comments by participants in seminars at the CREI-UPF Macro Workshop, MIT Macro Faculty Lunch, and Duke University. Anton Nakov provided excellent research assistance. We are grateful to Craig Burnside, Ellen McGrattan, Harald Uhlig, Jonas Fisher, and Susanto Basu for help with the data. Galí acknowledges financial support from DURSI (Generalitat de Catalunya), Fundación Ramón Areces, and the Ministerio de Ciencia y Tecnología (SEC2002–03816).
It is precisely that feature what differentiates the approach to identification in Galí (1999) from that in Blanchard and Quah (1989). The latter authors used restrictions on long-run effects on output, as opposed to labor productivity. In the presence of a unit root in labor input, that could lead to the mislabeling as “technology” shocks of any disturbances that were behind the unit root in labor input.
With four lags, the corresponding t-statistics are −2.5 and −7.08 for the level and the first-difference, respectively.
That distribution is obtained by means of a Montecarlo simulation based on 500 drawings from the distribution of the reduced-form VAR distribution.
Notice that the distribution of the impact effect on hours assigns a zero probability to an increase in that variable.
The latter evidence contrasts with their analysis of long-term U.S. data, in which the results vary significantly across samples and appear to depend on the specification used (more below).
Of course that was also the traditional view regarding technological change, but one that was challenged by the RBC school.
Exceptions include stochastic versions of endogenous growth models, as in King, Plosser, and Rebelo (1988b). In those models any transitory shock can in principle have a permanent effect on the level of capital or disembodied technology and, as a result, on labor productivity.
We are grateful to Craig Burnside and Ellen McGrattan for providing the data.
A similar conclusion is obtained by Fisher (2003), using a related approach in the context of the multiple technology shock model described below.
In particular, we use their “fully corrected” series from their 1999 paper. When revising the present paper BFK made us aware of an updated version of their technology series, extending the sample period through to 1996, and incorporating some methodological changes. The results obtained with the updated series were almost identical to the ones reported below.
That odds ratio increases substantially when an F-statistic associated with a covariates ADF test is incorporated as part of the encompassing analysis.
With the exception of their bivariate model under a level specification, CEV also find the contribution of technology shocks to the variance of output and hours at business cycles to be small (below 20 percent). In their bivariate level specification that contribution is as high as 66 percent for output and 33 percent for hours.
Given the previous observations one wonders how an identical prior for both specifications could be assumed, as CEV do when computing the odds ratio.
Unfortunately, CEV do not include any statistic associated with the null of no trend in hours in their encompassing analysis. While it is certainly possible that one can get a t-statistic as high as 8.13 on the time-squared term with a 13 percent frequency when the true model contains no trend (as their Monte Carlo analysis suggests), it must surely be the case that such a frequency is much higher when the true model contains the quadratic trend as estimated in the data!
Pesavento and Rossi (2003) propose an agnostic procedure to estimate the effects of a technology shock that does not require taking a stance on the order of integration of hours. They find that a positive technology shock has a negative effect on hours on impact.
We thank Jonas Fisher for kindly providing the data on real investment price.
This would be consistent with any model in which velocity is constant in equilibrium; see Galí (1999) for an example of such an economy.
Such a reduced-form relationship would naturally arise as an equilibrium condition of a simple RBC model with productivity as the only state variable.
The absence of another state variable (say, capital stock or other disturbances) implies a perfect correlation between the natural levels of output and employment, in contrast with existing RBC models in the literature where that correlation is positive and very high, but not one.
Throughout we assume that the condition κ(φπ – 1) + (1 – β)φy > 0 is satisfied. As shown by Bullard and Mitra (2002), that condition is necessary to guarantee a unique equilibrium.
This corresponds to the impact elasticity with respect to productivity, and ignores subsequent adjustment of capital (which is very small). The source is Table 3 in Campbell (1994), with an appropriate adjustment to correct for his (labor-augmenting) specification of techology in the production function (we need to divide Campbell’s number by 2/3).
Interestingly, a similar result can be uncovered in an unpublished paper by McGrattan (1999). Unfortunately the author did not seem to notice that finding (or, at least, she did not discuss it explicitly).
The analysis in GLV (2003) has been extended by Francis, Owyang, and Theodorou (2004) to other G-7 countries. They uncover substantial differences across countries in the joint response of employment, prices and interest rates to technology shocks, and argue that some of those differences can be grounded in differences in the underlying interest rate rules.
A less favorable assessment is found in Chang and Hong (2003), who conduct a similar exercise using four-digit U.S. manufacturing industries. Relying on evidence of sectoral nominal rigidities based on the work of Bils and Klenow (2002), they find weak evidence of contractionary effects and correlation with measures of price stickiness.
See Lettau and Uhlig (2000) for a detailed analysis of the properties of an RBC model with habit formation. As pointed out by Francis and Ramey, Lettau and Uhlig seem to dismiss the assumption of habits on the grounds that it yields “counterfactual cyclical behavior.”
However, the existing literature on estimating general equiilibrium models using Bayesian methods assumes that all shocks are stationary, even when highly correlated. A novelty of this paper is that we introduce a permanent technology shock. Ireland (2004) estimates a general equilibrium model with permanent technology shocks, using maximum likelihood.
A somewhat different estimation strategy is the one followed by Christiano, Eichenbaum, and Evans (2003), Altig and others (2003), and Boivin and Giannoni (2003), who estimate general equilibrium models by matching model’s implied impulse-response functions to the estimated ones.
Details can be found in an appendix available from the authors upon request.
subject to a usual budget constraint. The preference shock evolves, expressed in logarithms, as
Following Erceg and Levin (2003), we assume that the Federal Reserve reacts to output growth rather than to the output gap. An advantage of following such a rule, as Orphanides and Williams (2002) stress, is that mismeasurement of the level of potential output does not affect the conduct of monetary policy (as opposed to using some measure of detrended output to estimate the output gap).
If a random draw of the parameters is such that the model does not deliver a unique and stable solution, we assign a zero likelihood value, which implies that the posterior density will be zero as well. See Lubik and Schorfheide (2003) for an estimated DSGE model allowing for indeterminacy.
Rabanal (2003) finds a similar result for an estimated DSGE model that is only slightly different from the one used here.
We have also conducted some subsample stability analysis, splitting the sample into pre-Volcker years and the Volcker-Greenspan era. While there were some small differences in estimated parameters across samples, none of the main conclusions of this section were affected.
These second moments were obtained using a sample of 10,000 draws from the 500,000 that were previously obtained with the Metropolis-Hastings algorithm.
A related analysis has been carried out independently by Smets and Wouters (2003b), albeit in the context of a slightly different DSGE model.
The posterior mean and standard deviations are based on the same sample that was used to obtain the second moments.
A similar pattern of responses of output and hours to a technology shock can be found in Smets and Wouters (2003b).
We use the method of Ingram, Kocherlakota, and Savin (1994) to recover the structural shocks. This method is a particular case of using the Kalman filter to recover the structural shocks. We assume that the economy is at its steady-state value in the first observation, rather than assuming a diffuse prior. By construction, the full set of shocks replicate perfectly the features of the model.
In the one case where the VAR is identified correctly, it yields the correct qualitative responses, though with some quantitative bias resulting from the inability to capture the true dynamics with a low-order VAR. This result has been shown in Erceg, Guerrieri, and Gust (2004).
See Christiano, Eichenbaum, and Vigfusson (2003) for an illustration of the usefulness of that approach.