Reading between the Lines — Uncovering Asymmetry in the Central Bank Loss Function

The question is whether the central bank’s loss function is asymmetric – whether positive deviations of inflation from target are treated as more costly than negative deviations of the same size – and the paper argues the usual reaction-function route cannot answer it cleanly. In the optimal-policy literature preferences are “typically summarised through a quadratic loss function, which is U-shaped and symmetric around some pre-specified inflation target.” The paper notes that theory gives reasons to doubt this: Benigno and Rossi (2021) show that a welfare-based loss function going beyond the second-order approximation of household welfare in the basic New Keynesian model features asymmetry, and Yun (2005) implies that in the non-linear New Keynesian model inflation expansions generate larger distortions and welfare losses than contractions. Crucially, though, Benigno and Rossi (2021) also show that asymmetric preferences need not imply a correspondingly biased optimal policy – once the non-linearity of the aggregate supply equation is accounted for, optimal policy implies an overall expansionary bias. The authors draw the methodological consequence explicitly: “a reduced form estimation of the reaction function, as is usually done in the literature, does not necessarily allow for drawing direct inference on central bank preferences.”

Because asymmetric policy reactions can come from asymmetric preferences, from non-linearities in economic relationships, or from the effective lower bound, and these are non-trivial to tell apart empirically. Studies that infer loss-function asymmetry from an estimated reaction function have had to impose specific assumptions on the second and third channels: that the private sector is described by the non-policy block of a simple New Keynesian model, possibly with some non-linearity in the Phillips curve, and that monetary policy is not constrained by the effective lower bound. The paper’s claimed advantage is that estimating the loss function directly from communication “has the advantage that we do not have to make such specific assumptions concerning the economic relationships and the constraints on monetary policy.”

The corpus is the ECB’s introductory statements from press conferences after Governing Council monetary policy meetings, scraped from the ECB website, covering January 1999 to June 2021 – 238 meetings. The authors give two reasons for choosing the ECB. First, for the first two decades of the monetary union the definition of price stability “left open the question of whether the ECB would consider inflation rates above 2% to be more costly than rates below 2%, or equally so”: the 1998 formulation was a year-on-year HICP increase “below 2%”, clarified in 2003 to “below, but close to, 2% over the medium term.” Second, the ECB’s “carefully crafted, fixed-format introductory statements” after every policy meeting make an unusually comparable real-time text series – by contrast, the Federal Reserve’s post-FOMC press conferences only began in January 2019. Unlike individual governor speeches, the introductory statements “reflect views of all members of the Governing Council at the time policy decisions are made.” Meetings were monthly until December 2014 and eight times a year thereafter.

Two ways, plus further variants in robustness checks. The lexicon-based measure starts from the Loughran-McDonald (2011) finance dictionary and modifies it in four steps: adding British-English spellings, reclassifying as neutral the words that are technical terms in ECB usage rather than sentiment (the paper gives “stability” and “efficiency,” coded positive by Loughran-McDonald, and “lag” and “downward,” coded negative), classifying bigrams and trigrams containing a sentiment word (so that “greater confidence” and “greater uncertainty” are separated), and adding words found by cross-checking against FinBERT and by the authors’ own reading – among them “ample,” “robust” and “buoyant” as positive and “disequilibrium,” “tensions” and “contracted” as negative. Negations are handled asymmetrically and deliberately: only negations followed by positive words reverse the sentiment, on the reasoning that central banks soften bad news (“confidence has not improved”) rather than announce good news through negated negatives. The second measure uses FinBERT (Araci 2019), which returns the likelihood that a text’s tone is positive, negative or neutral; Central Bank RoBERTa (Pfeifer and Marohl 2023), which classifies tone as positive or negative, is used in robustness checks, as is the Economic Outlook Index of Picault and Renault (2017).

By Latent Dirichlet Allocation over paragraphs, treating each paragraph as a document. The authors set the number of topics to eight and select topics #3 and #6 as the inflation topics: in both, “inflation” is the second most common word, while “price stability” and “medium term” are among the most common terms in topic #3 and “price” and “hicp” among the top ten in topic #6. A paragraph is assigned to whichever topic has the highest probability. Pre-processing merges common multi-word terms into single tokens, drops paragraphs under ten words, removes greeting paragraphs, and removes stop words.

Tone is regressed on the inflation gap split at the de facto target by a dummy, giving a below-target slope and an above-target slope, with symmetry as a parameter restriction. The V-shaped specification is N_t = alpha + delta_B (pi_t - pi*)(1 - D_t) + delta_A (pi_t - pi*) D_t + beta’z_t + e_t, where D_t equals one when the real-time inflation estimate is above the target. The restriction delta_B + delta_A = 0 restores the symmetric specification, so the general form nests it, and symmetry is tested with an F-test on that restriction and with a likelihood ratio test against the restricted model. Real-time inflation is the latest monthly euro-area HICP rate published by Eurostat available at the time of each meeting – typically the flash estimate for the previous month. Controls are euro-area industrial production and unemployment (real-time), the spread of 6-month Euribor swaps and of euro-area corporate bond yields over government bond yields, and the Baker-Bloom-Davis Economic Policy Uncertainty index; because the financial and uncertainty series are unavailable early in the sample, specifications including them are estimated on 226 rather than 238 meetings.

The above-target slope is positive and significant at the 1% level in all twelve reported piecewise-linear specifications, while the below-target slope is significant in only four of them, and the above-target slope is much the larger in absolute value. In the benchmark specification using lexicon-based tone on whole statements with no controls, delta_B = -0.483 and delta_A = 1.531 (both significant at 1%), with the de facto target chosen at 2.00%; adding macro controls gives delta_B = -0.427 and delta_A = 1.579, and adding financial and uncertainty controls gives delta_B = -0.062 (insignificant) and delta_A = 0.871 (1%). The authors summarise: the absolute value of the slope “is typically roughly three times larger” above the de facto target than below it, “but in some specifications it is four, five or even six times larger,” and there are specifications where the left branch is essentially flat. The clearest such case is lexicon-based tone on inflation segments with the full control set, where delta_B = 0.057 does not differ from zero significantly while delta_A = 0.584 is significant at 1%. In all specifications, the above-target slope exceeds the below-target slope in absolute value.

Yes over the relevant range: symmetry is rejected in all specifications whenever the assumed target is 1.6% or higher. Because the de facto target is itself estimated by grid search, the authors also fix the target at each value in {1.3, 1.4, …, 2.0} and re-test the restriction. Symmetry is rejected in all specifications for targets of 1.6% and above, and in many specifications for every value in the grid – “especially in estimations where a FinBERT-based tone is used as the dependent variable.” The one reported specification in which the statistical tests do not confirm asymmetry is FinBERT tone on inflation segments with the full control set, where the grid-search target is 1.0%, at the lower bound of the search range; the authors observe it is “conceivable that the failure to find statistically significant support for asymmetry in this specification is related to the very low value” of the target.

Yes. The linear-exponential (Linex) specification, which nests the quadratic symmetric form, yields positive asymmetry parameters and rejects symmetry. The V-shape allows asymmetry but not convexity, so the authors also estimate by maximum likelihood a Linex loss in which a single parameter theta governs asymmetry, fixing the target at each grid value because three interacting parameters are hard to estimate jointly. With lexicon-based tone on whole statements, the estimated theta is positive throughout – for example 1.190 with no controls at a 2.0% target, 1.264 with macro controls, and 1.827 with the full control set – and the likelihood ratio test against the symmetric quadratic rejects at the 1% level for the higher target values. The Linex estimations fail to converge when FinBERT tone from inflation-focusing segments is the dependent variable, which the authors connect to that measure’s near-zero and sometimes positively signed below-target slope.

Below 2%, with the estimate depending on the tone measure: the lexicon-based approach points to 1.9% or 2.0%, the FinBERT-based estimates to “perhaps 1.7% or even lower.” In the asymmetric specifications using lexicon-based tone on whole statements the sum-of-squared-residuals criterion selects 2.00%; on inflation-focusing segments it selects 1.90%, which does not differ from 2.0% in a statistically significant way. With FinBERT tone the selected targets are lower and significantly below 2.0% – ranging from 1.5% to 1.7% on whole statements and 1.0% to 1.4% on inflation segments. The estimated targets from all four symmetric benchmark specifications are statistically significantly below 2.0%.

The authors report the asymmetry finding surviving changes to the controls, the inflation measure, the text used, the tone measure, the functional form, the data frequency, and the sample period. The inflation measure is varied across the latest observation, the average of the two latest observations, and the average of current inflation and a one-quarter-ahead forecast. The text is varied between whole introductory statements and inflation-focusing segments; the tone measure between the ECB-specific dictionary, FinBERT, Central Bank RoBERTa, and the Picault-Renault Economic Outlook Index; the loss function between piecewise-linear V-shaped and linear-exponential U-shaped; the frequency between meeting-based and quarterly. Sample variants drop the effective lower bound period, drop the Financial Crisis and Great Recession, and start the sample in May 2003 when the Governing Council clarified its definition of price stability. Forward-looking and backward-looking statements are analysed separately, with support for asymmetry in both.

It runs opposite to the Federal Reserve evidence and against the one comparable reaction-function study of the ECB. Shapiro and Wilson (2022), whose lexicon-based approach to estimating the FOMC’s loss function this paper builds on, find “some, albeit rather weak, evidence” that the Fed may have been more averse to low inflation than to high inflation – “clearly the opposite of what we find for the ECB.” Their focus was also different: with the Fed’s dual mandate, asymmetry was not their main object, and they were more concerned with estimating the Fed’s de facto target. On the ECB specifically, Surico (2007b) applies the reaction-function approach and “finds that the objective of price stability is symmetric, in clear contrast to our results.” Reaction-function studies by Hartmann and Smets (2018), Rostagno et al. (2021), Paloviita et al. (2021) and Maih et al. (2021) do find some evidence that the ECB may have responded more strongly to inflation above 2% than below, but Rostagno et al. and Paloviita et al. conclude that distinguishing this from symmetric responses around a lower inflation target is difficult. The paper also positions itself within the literature applying text mining to ECB communication, noting that none of those papers uses text analysis to study the Bank’s policy preferences.

They conclude that the ECB’s Governing Council “considered inflation rates above the target significantly more costly than below it during the first two decades of the euro area,” and they flag the post-2021 strategy as untested. They note the asymmetry has theoretical rationales in Benigno and Rossi (2021) and Yun (2005), and much earlier in Rogoff (1985), whose argument is that in the presence of inflationary bias society is better off appointing an inflation-conservative central banker. In July 2021 the Governing Council redefined its aim, stating that price stability is best maintained by aiming for 2% over the medium term with a commitment that “is symmetric (negative and positive deviations from this target are equally undesirable)” – explicitly dropping the below-2% bias and any remaining perception of 2% as a ceiling. The authors read that emphasis as also serving as a buffer against disinflationary shocks given reduced policy space at the effective lower bound and a low natural rate at the time, and say “future work should scrutinise whether the new strategy represents a significant change to the ECB’s preferences and policy relative to the old one as time passes.” The sample ends in June 2021, so the paper’s evidence speaks to the old framework only.