An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area

It builds and estimates a micro-founded model of the euro area, motivated by the practical need created by monetary union (Non-technical summary and Section 1, ECB Working Paper 171, pp. 5-7). “With the adoption of the euro and the start of the single monetary policy in EMU, there has been an increased need to understand the determinants of developments in the main aggregate euro area macro-economic time series.” The model’s frictions are described as ones that “appear to be necessary to capture the empirical persistence in the main euro area macro-economic data,” and the authors note that “many of these frictions have become quite standard in the SDGE literature.”

Staggered Calvo price and wage setting with partial indexation, variable capital utilisation, investment adjustment costs in the change of investment, and external habit formation (Section 1, p. 7). Sticky prices and wages follow Kollmann (1997) and Erceg, Henderson and Levin (2000); partial indexation of prices and wages that cannot be re-optimised “results in a more general dynamic inflation and wage specification that will also depend on past inflation.” Variable capital utilisation follows Greenwood, Hercowitz and Huffman (1988) and King and Rebelo (2000), and “tends to smooth the adjustment of the rental rate of capital in response to changes in output”; as in Christiano, Eichenbaum and Evans, the cost of adjusting utilisation is expressed in consumption goods, and the cost of adjusting the capital stock is a function of the change in investment “rather than the level of investment as is commonly done.” External habit formation “is used to introduce the necessary empirical persistence in the consumption process.”

In the number of structural shocks and in the estimation methodology; a footnote records that CEE “only consider the effects of a monetary policy shock” (Section 1, p. 7). The ten shocks are two “supply” shocks (productivity and labour supply), three “demand” shocks (preference, a shock to the investment adjustment cost function, and government consumption), three “cost-push” shocks (mark-ups in the goods and labour markets and a shock to the required risk premium on capital) and two monetary policy shocks. The authors elsewhere describe the equity-premium shock as “a shortcut to capture changes in” the required return on equity investment.

Seven series over 1970:1-1999:4 from the Fagan et al. (2001) area-wide database, with employment substituted for hours and capital variables treated as unobserved (Section 3, pp. 17-18). “As we do not have good measures of the area-wide capital stock, the value of capital or the rental rate on capital, we will assume these variables are not observed.” Because no consistent euro area series on aggregate hours exists, employment is used, with the assumption that only a constant fraction of firms can adjust employment to desired total labour input in any period, “the difference … taken up by (unobserved) hours worked per employer” – and since hours are assumed completely flexible, “the rigidity in employment does not affect the overall labour input.” All variables are treated as deviations around the sample mean, real variables detrended by a linear trend and inflation and the nominal rate by the same linear trend in inflation. A footnote adds that the first nine years of the sample are used to initialise the Kalman filter and are not used to estimate the structural parameters, with the authors noting that including them “would probably have implications for the stability of the policy rule” given the large monetary policy shocks.

Five steady-state-related parameters plus the wage mark-up, because the data are demeaned and the mark-up is unidentified (Section 3, p. 18). “A number of parameters were kept fixed from the start of the exercise. This can be seen as a very strict prior. Most of these parameters can be directly related to the steady-state values of the state variables and could therefore be estimated from the means of the observable variables … However, given that our data set is already demeaned, we can not pin them down.” The discount factor is set at 0.99 (an annual steady-state real rate of 4 percent), quarterly depreciation at 0.025 (10 percent annual), the capital share at 0.3 (a labour share of roughly 70 percent), the consumption share of output at 0.6 and investment at 0.22 (implying a steady-state capital-output ratio of about 2.2). The wage mark-up parameter is set at 0.5, “somewhat larger than the findings in the micro-econometric studies by Griffin (1996) based on US data.” Thirty-four further parameters are estimated.

On marginal likelihood the model has the highest posterior probability among the models considered, but the authors are careful about what that means (Section 3.3.1, pp. 20-23, and Table 2). The marginal likelihood integrates out the parameters and “gives an indication of the overall likelihood of the model given the data”; because it is directly related to the predictive density, it “also reflects the prediction performance of a model,” and the Bayes factor “compares the models’ ability to predict out of sample.” Against standard VARs of lag order one to three estimated on the same seven series, the model has the highest marginal probability, implying it “does the best job in predicting the seven variables over the period 1980:2 to 1999:4.” The authors explain the apparently paradoxical ranking of the VAR(3) – worst on marginal likelihood despite better in-sample statistics – by its parameter count relative to the short sample, and concede the point: “Of course, this result is dependent on the relatively small size of the observation period. For larger samples the natural disadvantage of the larger VAR(3) model will be offset to a greater extent by its extra explanatory power.” With a Minnesota prior the BVAR(3) “does almost as well as the SDGE model,” and the authors’ summary claim is correspondingly hedged: “the posterior odds suggest that the SDGE model outperforms most of the VAR models and does at least as well as the BVAR(3) model.”

The data covariances generally fall within the model’s error bands, but those bands are wide, and the interest rate correlations are the weak point (Section 3.3.2, pp. 23-24, and Graph 2). Empirical cross-covariances come from a VAR(3) on 115 observations covering 1971:q2-1999:q4; model-based ones from the same VAR(3) fitted to 10,000 simulated samples of the same length. “Generally, the data covariances fall within the error bands, suggesting that the model is indeed able to mimick the cross-covariances in the data. However, the error bands are quite large.” The authors turn this into a methodological point: “these large error bands are often neglected in more traditional calibration exercises of SDGE models, in which models are often rejected on the basis of an informal comparison of model-based and empirical moments. It appears that the uncertainty coming from the short sample, is significantly higher than that coming from parameter uncertainty.” They also flag the specific failure: “the cross-correlations with the interest rate do not seem to be fully satisfactory. The estimated variance of the interest rate is too small.”

Indexation is weaker than the prior, Calvo stickiness is considerable, and prices are estimated to be stickier than wages – an ordering the authors treat as a possible artefact of their marginal cost specification (Section 3.2, pp. 21-22). “The average duration of wage contracts is estimated to be one year, whereas the average duration of the price contracts is much longer at two and a half years. The greater stickiness in prices relative to wages is somewhat counterintuitive, but turns out to be a very robust outcome of the estimated model. In spite of our relatively tight prior on the Calvo price parameter the data prefer a much higher degree of stickiness.” The proposed explanation is specification, not economics: individual households’ marginal cost of supplying labour slopes upward, but the intermediate goods marginal cost curve is assumed flat under constant returns to scale, and “for a given elasticity of prices to real marginal cost, this will tend to bias upward the estimate of Calvo price stickiness.” The authors support this by noting that Gali, Gertler and Lopez-Salido find the same high price stickiness for the euro area under constant returns, and “only when they assume decreasing returns to scale and an upward-sloping marginal cost curve” do they estimate a degree comparable to what is found here for wages.

An intertemporal elasticity of substitution below one, substantial external habit, modest investment responsiveness, and a poorly identified but high labour supply elasticity (Section 3.2, pp. 22-23). The intertemporal elasticity of substitution is less than one, close to the range assumed in the RBC literature, though the authors caution that “one needs to be careful when making such comparisons, as we have assumed external habit formation which turns out to be significant.” The external habit stock is estimated at 55 percent of past consumption, “somewhat smaller than the estimates reported in CEE (2001).” Together the habit and substitution estimates imply that an expected one percent rise in the short-term rate sustained for four quarters reduces consumption by about 0.28. The investment adjustment cost estimate implies investment rises about 0.2 percent following a one percent rise in the current price of installed capital. The labour supply elasticity is estimated to be relatively large, but “this parameter is not very precisely estimated.”

It satisfies the Taylor principle with substantial smoothing, but the authors flag that there was no single euro area monetary policy over the sample (Section 3.2, p. 23). “Obviously, as there was no single monetary policy in the euro area over the estimation period, these results need to be taken with a grain of salt.” Subject to that, “the estimates imply that in the long run the response of interest rates to inflation was greater than one and close to the value suggested by Taylor (1993), thereby satisfying the so-called Taylor principle. Also the response to output is similar to the one suggested by Taylor (1993).” There is in addition a significant positive short-run reaction to the current change in inflation and the current real growth rate, a negative response to positive productivity and labour supply shocks, and “a substantial degree of interest rate smoothing.”

A hump-shaped fall in output, consumption and investment after a temporary tightening, with a markedly different pattern for a persistent change in the inflation objective (Section 4.1, pp. 24-25). The temporary shock raises the nominal and real short rate and produces hump-shaped falls in output, consumption and investment, with real wages falling and “the maximum effect on investment … about three times as large as that on consumption.” The authors note the price effects “are somewhat larger than those estimated in some identified VARs.” For a persistent change in the inflation objective there is “no liquidity effect, as nominal interest rates start falling immediately as a result of the reduced inflation expectations” – consistent with Gali’s argument that the presence of a liquidity effect depends on the shock’s persistence – and because the change is gradual and expectations adjust, “the output effects of the change in inflation are much smaller.”

Preference, labour supply and monetary policy shocks at medium to long horizons; price mark-up shocks for short-run inflation; productivity only modestly for output (Section 4.2, pp. 25-27, and Table 3, with horizons of 1 year, 2.5 years and 25 years). At one year output is driven primarily by the preference and monetary policy shocks; in the medium term both continue to dominate while the two supply shocks together account for about 20 percent; in the long run the labour supply shock dominates but “somewhat surprisingly the monetary policy shock still accounts for about one fourth of the forecast error in output,” working mainly through investment. The authors confront the contrast with the identified-VAR literature directly: the supply shocks accounting for only 37 percent in the long run “seems to run counter to the results from identified VAR studies,” but “it should be noted that in those studies it is assumed that only supply shocks affect output in the long run.” The limited role of productivity – “maximum 12% of forecast error variance in output” – is read as confirming Gali’s conjecture that the negative output-employment correlation after a productivity shock “raises serious doubts about the quantitative significance of productivity shocks as a source of aggregate fluctuations.” Short-run inflation is driven mainly by price mark-up shocks, which the authors note “could capture a whole range of shocks that are not accounted for in the stylised model such as changes in oil prices, terms-of-trade shocks, changes in taxes.” They add an important caveat about interpretation: the decomposition “does not say anything about the fundamentally monetary nature of inflation in the long run,” because the model’s steady state is deterministic so the long-run variance is necessarily determined by temporary shocks.

A significant contribution to the 1970s inflation surge and to its stabilisation from the 1980s, and little to output variation after the mid-1980s (Section 4.3, pp. 27-28). “Monetary policy has clearly contributed quite significantly to the surge in inflation in the 1970s and its stabilisation from 1980s onward.” On output: “While loose monetary policy contributed to offsetting the fall in output due to negative supply and demand shocks in the 1970s, it contributed very little to output variations in the 1980s and 1990s, although the monetary policy tightening during the ERM crisis of 1992 has contributed somewhat to the 1993 recession.” The authors preface the exercise with a warning that “obviously such a decomposition must be treated with caution.”

As the flexible-price-and-wage level of output that would arise in the absence of mark-up shocks, because three of the model’s shocks are inefficient mark-up variations (Section 5, pp. 28-29). In Woodford’s benchmark with only price rigidities and no mark-up shocks, optimal policy replicates the flexible-price equilibrium and the flexible-price gaps are useful policy indicators; with both price and wage rigidities Erceg, Henderson and Levin show that targeting a weighted average of price and wage inflation, or of price inflation and the output gap, “comes close to optimal monetary policy.” But here the wage mark-up, price mark-up and equity premium shocks “give rise to inefficient variations in the flexible-price-and-wage level of output,” so “one can argue that monetary authorities should not accommodate such variations and instead try to keep output at its efficient level.” The authors state the consequence plainly: “Of course, in this case mark-up shocks will give rise to a trade-off between inflation stabilisation and output gap stabilisation.”

Natural output responds strongly to demand as well as supply shocks, while the real wage is nearly flat except after productivity shocks, because both labour demand and labour supply schedules are estimated to be flat (Section 5, pp. 29-31, Graphs 15-19). Under flexible prices a productivity shock raises output sharply and real wages immediately, but employment falls as households cut labour supply in line with the fall in the marginal utility of consumption. A positive preference shock makes natural output “respond strongly negatively,” because higher consumption reduces the marginal benefit from working, cutting labour supply, reducing the marginal product of capital and, with a higher natural real rate, depressing investment. The flatness explanation is explicit: “The labour demand schedule (45) is flat because of the low estimated elasticity of the cost of adjusting capacity utilisation, while the labour supply schedule (46) is flat because of the high estimate of the labour supply elasticity,” so shifts in either schedule move employment a lot and the real wage little, and “due to the strong consumption effect on labour supply, also ‘demand’ shocks can have a relatively strong impact on employment and the output level.”

That the confidence bands are wide, and that the real interest rate gap in particular may be useless for policy (Section 5, pp. 31-32, Graphs 20-21). “While the confidence bands around both the output and the interest rate gap are quite large, this is particularly problematic for the real interest rate gap, which is hardly significant over the sample period. This suggests that the real interest rate gap may be a poor guide for monetary policy.” The estimated potential output path “is very different from traditional estimates which rely on a smoothed trend through output”: a dramatic fall from 1973 to 1975 produces a significant positive output gap through most of the 1970s and early 1980s, coinciding with the rise in inflation, followed by a gradual rise from 1982 with a dip in the early 1990s and a substantial negative gap remaining at the end of 1999. Most of the long-term variation in potential output is attributed to labour supply developments, and by the real interest rate gap “monetary policy was relatively tight during the last seven years of the 1990s, although most recently the gap seems to have closed.”

That they are rich enough to describe the data, conditional on entertaining enough shocks (Non-technical summary and Section 3.3.1, pp. 5-6, 23). “These results show that the current generation of New-Keynesian SDGE models with sticky prices and wages and endogenous persistence in consumption and investment are able to capture the main features of the euro area data, as long as one is willing to entertain enough structural shocks to capture the stochastics.” The conditional clause is the load-bearing part: the claim is about the model class augmented with ten orthogonal disturbances, not about the frictions alone. The authors also situate the result against a literature in which “in most of these cases the SDGE model is clearly rejected,” citing Schorfheide’s very low Bayes factors for small two-shock models tested on two variables.