https://robinchen.org/tag/tvp-var/TVP-VARHugo Blox Builder (https://hugoblox.com)en-usWed, 11 Aug 2021 00:00:00 +0000https://robinchen.org/media/logo_hu9727855325976137109.pnghttps://robinchen.org/tag/tvp-var/https://robinchen.org/publication/divisia-puzzle/Wed, 11 Aug 2021 00:00:00 +0000https://robinchen.org/publication/divisia-puzzle/<script type="application/ld+json"> { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "Why does the U.S. price puzzle persist in modern-sample VARs even with commodity prices and futures data?", "acceptedAnswer": { "@type": "Answer", "text": "The price puzzle persists in post-1988 U.S. data because the federal funds rate has lost much of its identifying power for monetary policy shocks in an environment of heightened Fed transparency, forward guidance, and a near-zero neutral rate. Chen and Valcarcel (2021) test every standard fix — commodity prices (CRB and IMF indices), 30-day federal funds futures, forward rates from overnight repo spreads — across 23 different federal funds rate specifications spanning 1988-2020 and find the price puzzle remains. This contrasts with Christiano, Eichenbaum and Evans (1999), who established that commodity prices resolve the puzzle in a 1965-1995 sample. Barakchian and Crowe (2013) confirm that monetary policy post-1988 became more forward-looking, invalidating identifying assumptions of conventional methods. Chen and Valcarcel call this the 'modern-sample price puzzle.'" } }, { "@type": "Question", "name": "Does replacing the federal funds rate with a Divisia monetary aggregate resolve the price puzzle in a modern sample?", "acceptedAnswer": { "@type": "Answer", "text": "Yes. Chen and Valcarcel (2021) show that replacing the Wu-Xia shadow federal funds rate with Divisia M4 or Divisia M2 produces sensible, theory-consistent price and output responses in every specification they examine — including three-variable VARs that contain no commodity prices and no futures data. This is Divisia-sufficiency: the Divisia aggregate resolves the puzzle by itself. The result builds on Belongia (1996), who demonstrated that replacing simple-sum with Divisia reverses qualitative inference across major studies, and on Keating, Kelly, Smith and Valcarcel (2019), who showed Divisia M4 identification delivers plausible responses in a historical sample. Chen and Valcarcel extend the result to the post-1988 modern period." } }, { "@type": "Question", "name": "How does the transmission of monetary policy to money markets differ between the federal funds rate and Divisia M4 after 2008?", "acceptedAnswer": { "@type": "Answer", "text": "After 2008, expansionary federal funds rate shocks generate puzzlingly contractionary money-market responses — balances in currency, demand deposits, savings, repos, commercial paper, and T-bills all fall. Expansionary Divisia M4 shocks produce sensible expansionary responses, and the less-liquid assets (IMMFs, large time deposits, repos, CP, T-bills) respond with larger magnitudes than the highly liquid ones. Chen and Valcarcel (2021) interpret this as post-crisis flight-to-safety transmission: households moved into savings, firms into less-liquid but safer instruments, and the Fed's large-scale asset purchases mechanically expanded the T-bill and repo components of Divisia M4. The magnitude ordering — less-liquid assets responding more than currency and demand deposits — is a distinctive signature of the modern monetary transmission mechanism invisible to short-rate specifications." } }, { "@type": "Question", "name": "Can commodity prices or federal funds futures rescue the short-rate specification in a modern sample?", "acceptedAnswer": { "@type": "Answer", "text": "No. Chen and Valcarcel (2021) test the CRB commodity index, the IMF global index, the 30-day federal funds futures rate, and the Brissimis-Magginas overnight-repo-spread forward rate across 23 federal funds rate specifications spanning 1988-2020. The price puzzle remains pervasive throughout. This is consistent with Barakchian and Crowe (2013) and Ramey (2016). The failure is not informational — it is indicator-related: increased Fed transparency and a near-zero neutral rate have shrunk the unanticipated component of federal funds rate movements that SVARs need to identify a shock." } }, { "@type": "Question", "name": "Should I use the Wu-Xia shadow federal funds rate to identify monetary policy shocks in a post-2008 sample?", "acceptedAnswer": { "@type": "Answer", "text": "Use it with caution. Wu and Xia (2016) proposed the shadow rate to extend the federal funds series through the effective-lower-bound period, but Chen and Valcarcel (2021) find it produces persistent price puzzles across 23 modern-sample specifications, and the resulting shocks transmit implausibly through money markets. Krippner (2020) separately documents that shadow-rate estimates are sensitive to minor modeling choices, and those sensitivities propagate into wide variations in inferred UMP effects. For a modern-sample VAR, Divisia M4 as the indicator resolves the puzzles the shadow rate cannot." } }, { "@type": "Question", "name": "What is the Divisia monetary aggregate and why does it matter for monetary policy identification?", "acceptedAnswer": { "@type": "Answer", "text": "Divisia monetary aggregates weight each component of the money stock by its user cost, recognizing that currency, demand deposits, savings, money-market funds, and T-bills provide different flows of liquidity services and have different opportunity costs. Simple-sum aggregates (M1, M2) treat all components as perfect substitutes — the Barnett critique. Belongia (1996) showed empirically that Divisia reverses qualitative inference across major studies, and Belongia and Ireland (2014) formalized the Barnett critique inside a New Keynesian model. Chen and Valcarcel (2021) use Divisia M4 — the 15-component broadest U.S. aggregate, including institutional money funds, large time deposits, repos, commercial paper, and T-bills — as the policy indicator in their modern-sample VAR. The data come from the Center for Financial Stability. Belongia and Ireland (2019) document a stable Divisia money demand function over 1967-2019, undermining claims of inherent money-demand instability." } } ] } </script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "ScholarlyArticle", "headline": "Monetary transmission in money markets: The not-so-elusive missing piece of the puzzle", "author": [ { "@type": "Person", "name": "Zhengyang Chen", "affiliation": { "@type": "Organization", "name": "University of Northern Iowa, Wilson College of Business" }, "url": "https://www.robinchen.org/", "email": "zhengyang.chen@uni.edu" }, { "@type": "Person", "name": "Victor J. Valcarcel", "affiliation": { "@type": "Organization", "name": "The University of Texas at Dallas, School of Economic, Political and Policy Sciences" } } ], "datePublished": "2021-08-12", "isPartOf": { "@type": "PublicationIssue", "issueNumber": "131", "datePublished": "2021-10", "isPartOf": { "@type": "Periodical", "name": "Journal of Economic Dynamics and Control", "issn": "0165-1889" } }, "identifier": { "@type": "PropertyValue", "propertyID": "DOI", "value": "10.1016/j.jedc.2021.104214" }, "url": "https://doi.org/10.1016/j.jedc.2021.104214", "keywords": [ "price puzzle", "Divisia money", "Divisia M4", "interest rate pass-through", "time-varying-parameter vector autoregressions", "TVP-VAR", "time-varying-parameter factor-augmented vector autoregressions", "TVP-FAVAR", "unexpected monetary policy shocks", "modern-sample price puzzle", "Divisia-sufficiency", "post-crisis flight-to-safety transmission" ], "about": [ "Monetary policy identification", "Federal funds rate", "Divisia monetary aggregates", "Money markets", "Post-2008 monetary transmission", "Wu-Xia shadow rate", "Barnett critique", "Price puzzle" ], "abstract": "Chen and Valcarcel (2021) investigate monetary policy shocks from alternative policy indicators in a modern U.S. sample (1988-2020). The Wu-Xia shadow federal funds rate produces persistent price puzzles that are not resolved by the standard fixes — commodity prices, federal funds futures, or forward rates. Replacing the shadow rate with Divisia M4 or Divisia M2 resolves the puzzle without these fixes (Divisia-sufficiency). Transmission to money markets post-2008 exhibits a flight-to-safety pattern: less-liquid assets (IMMFs, LTDs, repos, CP, T-bills) respond more strongly than currency and demand deposits under Divisia shocks, while federal funds rate shocks produce implausibly contractionary money-market responses throughout. The paper introduces the concepts of the modern-sample price puzzle, Divisia-sufficiency, and post-crisis flight-to-safety transmission." } </script> <h2 id="in-a-modern-us-sample-the-federal-funds-rate-is-no-longer-a-reliable-monetary-policy-indicator--but-a-broad-divisia-monetary-aggregate-is">In a Modern U.S. Sample, the Federal Funds Rate Is No Longer a Reliable Monetary Policy Indicator — but a Broad Divisia Monetary Aggregate Is</h2> <p><strong>TL;DR:</strong> The price puzzle — contractionary monetary policy raising prices in VAR models — has resisted every standard fix in post-1988 U.S. data. <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021, <em>Journal of Economic Dynamics and Control</em>)</a> show that swapping the Wu-Xia shadow rate for Divisia M4 resolves the puzzle without any ad hoc fixes, and reveals a post-2008 flight-to-safety pattern in which less-liquid money markets respond more strongly than currency and demand deposits. The problem was never the omitted information — it was the indicator itself.</p> <h2 id="key-concepts">Key Concepts</h2> <dl> <dt><strong>Modern-sample price puzzle</strong></dt> <dd>The post-1988 incarnation of the price puzzle that, unlike the historical version, is <em>not</em> resolved by the Christiano-Eichenbaum-Evans remedies (commodity prices, fed funds futures, forward rates). Coined by <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021)</a> .</dd> <dt><strong>Divisia-sufficiency</strong></dt> <dd>The result that, in a modern-sample VAR, replacing the short-term rate with a Divisia monetary aggregate is by itself sufficient to restore theory-consistent responses of prices and output, even without commodity prices or futures data. <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021)</a> .</dd> <dt><strong>Post-crisis flight-to-safety transmission</strong></dt> <dd>The finding that post-2008, less-liquid assets (IMMFs, large time deposits, repos, commercial paper, T-bills) respond with larger magnitudes than currency and demand deposits to an expansionary Divisia M4 shock — the opposite of the contractionary, liquidity-preserving pattern produced by shadow-rate shocks. <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021)</a> .</dd> </dl> <hr> <h2 id="q1-why-does-the-us-price-puzzle-persist-in-modern-sample-vars-even-with-commodity-prices-and-futures-data">Q1. Why does the U.S. price puzzle persist in modern-sample VARs even with commodity prices and futures data?</h2> <p><strong>The price puzzle persists in post-1988 U.S. data because the federal funds rate — conventionally augmented with commodity prices, fed funds futures, or forward rates — has lost much of its identifying power for monetary policy shocks in an environment of heightened Fed transparency, forward guidance, and a near-zero neutral rate. The problem is not the omitted information; it is the indicator itself.</strong></p> <p><a href="https://doi.org/10.1016/S1574-0048%2899%2901005-8">Christiano, Eichenbaum and Evans established that including commodity prices in a recursive VAR eliminates the price puzzle in a sample spanning 1965-1995</a> , and <a href="https://doi.org/10.1016/S0304-3932%2801%2900055-1">Kuttner introduced the use of fed funds futures data to separate anticipated from unanticipated target changes</a> . <a href="https://doi.org/10.1016/j.jmoneco.2005.05.014">Brissimis and Magginas argued that augmenting VARs with forward-looking variables such as futures and forward rates resolves the puzzle</a> . <a href="https://doi.org/10.1162/0033553053327452">Bernanke, Boivin and Eliasz proposed factor-augmented VARs as a more comprehensive information-set fix</a> .</p> <p><a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021) show that every one of these fixes fails in a 1988-2020 sample</a> . Across 23 iterations of the federal funds rate specification — combining real output measures (IP, CFNAI, monthly RGDP), price levels (PCE, CPI, core variants), commodity prices (CRB, IMF), and federal funds futures or forward rates — price puzzles remain pervasive, both in time-varying-parameter VARs and in constant-parameter counterparts. This is the <strong>modern-sample price puzzle</strong>.</p> <p>Consistent with this, <a href="https://doi.org/10.1016/j.jmoneco.2013.09.006">Barakchian and Crowe find that monetary policy post-1988 became more forward-looking, invalidating the identifying assumptions in conventional methods</a> , and <a href="https://doi.org/10.1016/bs.hesmac.2016.03.003">Ramey&rsquo;s Handbook synthesis confirms the preponderance of puzzles across post-1983 identification schemes</a> .</p> <p><strong>Why the standard fixes fail:</strong> A neutral federal funds rate with enough room for material movement is a prerequisite for the short-rate indicator to work. The post-2008 effective-lower-bound period, combined with decades of increasingly transparent Fed communication and forward guidance, has squeezed the unanticipated component of federal funds rate movements toward zero — the thing SVARs need to identify a shock.</p> <hr> <h2 id="three-approaches-to-monetary-policy-indicator-in-a-modern-us-sample-1988-2020">Three Approaches to Monetary Policy Indicator in a Modern U.S. Sample (1988-2020)</h2> <table> <thead> <tr> <th style="text-align: left">Dimension</th> <th style="text-align: left">Short Rate + Commodity Prices (CEE 1999)</th> <th style="text-align: left">Short Rate + Futures/Forward Rates (Brissimis-Magginas 2006)</th> <th style="text-align: left">Divisia M4 (Chen-Valcarcel 2021)</th> </tr> </thead> <tbody> <tr> <td style="text-align: left"><strong>Core claim</strong></td> <td style="text-align: left">Commodity prices proxy the Fed&rsquo;s forward-looking information set and resolve the price puzzle.</td> <td style="text-align: left">Forward-looking variables (fed funds futures, forward rates) reflect market expectations of policy and resolve the price puzzle.</td> <td style="text-align: left">The short rate has lost identifying power in the modern sample; a Divisia monetary aggregate is the correct policy indicator.</td> </tr> <tr> <td style="text-align: left"><strong>Key references</strong></td> <td style="text-align: left"><a href="https://doi.org/10.1016/S1574-0048%2899%2901005-8">Christiano, Eichenbaum &amp; Evans (1999)</a> , <a href="https://doi.org/10.1162/0033553053327452">Bernanke, Boivin &amp; Eliasz (2005)</a> </td> <td style="text-align: left"><a href="https://doi.org/10.1016/S0304-3932%2801%2900055-1">Kuttner (2001)</a> , <a href="https://doi.org/10.1257/000282802320189069">Cochrane &amp; Piazzesi (2002)</a> , <a href="https://doi.org/10.1016/j.jmoneco.2005.05.014">Brissimis &amp; Magginas (2006)</a> , <a href="https://doi.org/10.1257/mac.20130329">Gertler &amp; Karadi (2015)</a> </td> <td style="text-align: left"><a href="https://doi.org/10.1086/262052">Belongia (1996)</a> , <a href="https://doi.org/10.1016/j.jeconom.2014.06.006">Belongia &amp; Ireland (2014)</a> , <a href="https://doi.org/10.1111/jmcb.12522">Keating, Kelly, Smith &amp; Valcarcel (2019)</a> , <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen &amp; Valcarcel (2021)</a> </td> </tr> <tr> <td style="text-align: left"><strong>Testable prediction</strong></td> <td style="text-align: left">Including commodity prices eliminates the price puzzle across samples.</td> <td style="text-align: left">Including futures or forward rates eliminates the price puzzle.</td> <td style="text-align: left">Divisia M4 as the indicator eliminates the price puzzle <em>without</em> commodity prices or futures.</td> </tr> <tr> <td style="text-align: left"><strong>Empirical verdict in modern sample (1988-2020)</strong></td> <td style="text-align: left"><strong>Fails.</strong> <a href="https://doi.org/10.1016/j.jedc.2021.104214">Price puzzle persists across 23 iterations of the federal funds rate specification with commodity prices</a> .</td> <td style="text-align: left"><strong>Fails.</strong> <a href="https://doi.org/10.1016/j.jedc.2021.104214">Price puzzle remains even with 30-day fed funds futures, CRB or IMF commodity indices, or forward rates constructed from overnight repo spreads</a> .</td> <td style="text-align: left"><strong>Succeeds.</strong> <a href="https://doi.org/10.1016/j.jedc.2021.104214">Divisia M4 resolves the puzzle across 23 specifications, including three-variable VARs with no commodity prices and no futures</a> .</td> </tr> <tr> <td style="text-align: left"><strong>Policy transmission to money markets</strong></td> <td style="text-align: left">Puzzlingly contractionary responses for currency, deposits, repos, CP, T-bills post-2008.</td> <td style="text-align: left">Same contractionary puzzles as commodity-prices specification; futures/forward rates do not rescue transmission.</td> <td style="text-align: left">Sensible expansionary responses; less-liquid assets respond <em>more strongly</em> than currency/DDs post-2008 (flight-to-safety).</td> </tr> <tr> <td style="text-align: left"><strong>Sample-period applicability</strong></td> <td style="text-align: left">Works for historical samples (1960s-1990s); breaks down after 1988.</td> <td style="text-align: left">Works to varying degrees in historical samples; breaks down after 1988.</td> <td style="text-align: left">Designed for the modern sample; also works historically (<a href="https://doi.org/10.1111/jmcb.12522">Keating, Kelly, Smith &amp; Valcarcel 2019</a> ).</td> </tr> <tr> <td style="text-align: left"><strong>Named concept</strong></td> <td style="text-align: left">CEE identification / commodity-prices fix</td> <td style="text-align: left">Forward-looking-variables identification</td> <td style="text-align: left"><strong>Divisia-sufficiency</strong> · <strong>Modern-sample price puzzle</strong> · <strong>Post-crisis flight-to-safety transmission</strong> (<a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen &amp; Valcarcel 2021</a> )</td> </tr> </tbody> </table> <hr> <h2 id="q2-does-replacing-the-federal-funds-rate-with-a-divisia-monetary-aggregate-resolve-the-price-puzzle-in-a-modern-sample">Q2. Does replacing the federal funds rate with a Divisia monetary aggregate resolve the price puzzle in a modern sample?</h2> <p><strong>Yes. Replacing the Wu-Xia shadow federal funds rate with Divisia M4 (or the narrower Divisia M2) produces sensible, theory-consistent price responses in every specification Chen and Valcarcel examine — including three-variable VARs that contain no commodity prices and no futures data. This is Divisia-sufficiency: the Divisia aggregate does the heavy lifting by itself.</strong></p> <p>The foundation for this result rests on the Barnett critique. <a href="https://doi.org/10.1086/262052">Belongia demonstrated that replacing simple-sum aggregates with Divisia indexes reverses the qualitative inference of four out of five influential studies on the effects of money</a> , and <a href="https://doi.org/10.1016/j.jeconom.2014.06.006">Belongia and Ireland formalized within a New Keynesian model that &ldquo;measurement matters&rdquo; — a Divisia quantity tracks the true monetary aggregate almost perfectly while simple-sum does not</a> . <a href="https://doi.org/10.1111/jmcb.12522">Keating, Kelly, Smith and Valcarcel extended this to a VAR framework, showing Divisia M4 identification delivers plausible responses free of price, output, and liquidity puzzles in a historical sample</a> .</p> <p><a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021) extend the Divisia result to the post-1988 modern sample</a> . Across three-variable TVP-VARs and larger TVP-FAVARs, specifications with DM4 or DM2 as the indicator yield:</p> <ol> <li>A <em>gradual</em> (and correctly-signed) price level response consistent with New Keynesian sticky-price predictions.</li> <li>Theory-consistent real output responses across PCE, CPI, core price measures, and three alternative output indicators.</li> <li>Resolution that holds even when commodity prices and federal funds futures are <em>excluded</em> from the VAR — unlike the Christiano-Eichenbaum-Evans recipe, Divisia does not require these crutches.</li> <li>Quantitatively larger post-2008 price responses for DM4 than for DM2, consistent with DM4 capturing a wider array of the monetary shocks that eventually pass through to prices.</li> </ol> <p>This aligns with <a href="https://doi.org/10.1016/j.jmacro.2019.103128">Belongia and Ireland&rsquo;s finding of a stable Divisia money demand relationship in the modern sample</a> , which is the microfounded underpinning for why a Divisia aggregate can serve as a policy indicator.</p> <hr> <h2 id="q3-how-does-the-transmission-of-monetary-policy-to-money-markets-differ-between-the-federal-funds-rate-and-divisia-m4-after-2008">Q3. How does the transmission of monetary policy to money markets differ between the federal funds rate and Divisia M4 after 2008?</h2> <p><strong>After 2008, expansionary federal funds rate shocks generate puzzlingly contractionary money-market responses — balances in currency, demand deposits, savings, repos, commercial paper, and T-bills all <em>fall</em>. Expansionary Divisia M4 shocks, by contrast, produce sensible expansionary responses, and the <em>less-liquid</em> assets (IMMFs, large time deposits, repos, CP, T-bills) respond with <em>larger</em> magnitudes than the highly liquid ones. Chen and Valcarcel call this post-crisis flight-to-safety transmission.</strong></p> <p>The standard VAR approach places money below interest rates and output. <a href="https://doi.org/10.1162/0033553053327452">Bernanke, Boivin and Eliasz&rsquo;s FAVAR treatment orders the rate indicator last and restricts monetary assets not to respond within the period</a> , while <a href="https://doi.org/10.1111/jmcb.12522">Keating, Kelly, Smith and Valcarcel instead order the indicator before the monetary block, allowing money markets to respond freely to policy</a> . Chen and Valcarcel adopt the latter block-recursive approach, letting 14 different deposits and money-market instruments respond unrestricted.</p> <p><a href="https://doi.org/10.1016/j.jedc.2021.104214">The results are stark</a> . Under the Wu-Xia shadow federal funds rate:</p> <ul> <li>Currency, demand deposits, and OCDs respond negatively to an expansionary shock, particularly after 2008.</li> <li>Savings at banks and thrifts — counterintuitively — also contract.</li> <li>IMMFs, repos, and T-bills show large <em>negative</em> responses post-crisis, which is the opposite sign from theory.</li> </ul> <p>Under Divisia M4, the same specifications yield:</p> <ul> <li>Sensible positive responses for currency and demand deposits.</li> <li>Larger positive responses for savings at banks and thrifts (consistent with higher household personal saving after 2008).</li> <li>Even larger positive responses for less-liquid assets — IMMFs, LTDs, repos, CP, T-bills — commensurate with savings rather than with currency.</li> </ul> <p>The post-2008 magnitude pattern across asset classes is consistent with a flight-to-safety channel: households moved into savings, firms moved into less-liquid but safer instruments (time deposits, repos against Treasury collateral), and the Fed&rsquo;s large-scale asset purchases mechanically expanded Treasury holdings in the monetary aggregate.</p> <hr> <h2 id="q4-can-commodity-prices-or-federal-funds-futures-rescue-the-short-rate-specification-in-a-modern-sample">Q4. Can commodity prices or federal funds futures rescue the short-rate specification in a modern sample?</h2> <p><strong>No. Commodity prices (both CRB and IMF indices), the 30-day federal funds futures rate, and the Brissimis-Magginas overnight-repo-spread forward rate all fail to resolve the modern-sample price puzzle when the Wu-Xia shadow federal funds rate is the indicator. The puzzle-fix-fails-in-modern-data pattern holds across 23 specifications.</strong></p> <p><a href="https://doi.org/10.1016/S1574-0048%2899%2901005-8">Christiano, Eichenbaum and Evans concluded that including commodity prices was needed to resolve the puzzle in a 1965-1995 sample</a> , and <a href="https://doi.org/10.1257/000282802320189069">Cochrane and Piazzesi argued that high-frequency identification from daily target-change surprises avoids the omitted-variable problem of monthly VARs</a> . <a href="https://doi.org/10.1016/j.jmoneco.2005.05.014">Brissimis and Magginas advocated specifically for federal funds futures or forward rates in a recursive VAR</a> , while <a href="https://doi.org/10.1257/mac.20130329">Gertler and Karadi popularized the use of high-frequency surprises as external instruments in proxy SVARs</a> .</p> <p><a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel test all of these within a common TVP-FAVAR framework and find the price puzzle remains</a> . The envelope of impulse responses across 23 different federal funds rate specifications — crossing three output measures, four price indices, two commodity indices, and futures/forward rate variants — shows a generally pervasive price puzzle throughout the 1988-2020 sample, with no specification consistently escaping it. <a href="https://doi.org/10.1016/j.jmoneco.2013.09.006">This matches the Barakchian-Crowe finding that a forward-looking Fed invalidates post-1988 identifying assumptions</a> and <a href="https://doi.org/10.1016/bs.hesmac.2016.03.003">Ramey&rsquo;s broader synthesis</a> .</p> <p>The takeaway for practitioners: If your sample begins in the late 1980s or later and you must use a short-term rate, expect puzzles. If you use Divisia M4 instead, the puzzles disappear even without commodity prices or futures.</p> <hr> <h2 id="q5-should-i-use-the-wu-xia-shadow-federal-funds-rate-to-identify-monetary-policy-shocks-in-a-post-2008-sample">Q5. Should I use the Wu-Xia shadow federal funds rate to identify monetary policy shocks in a post-2008 sample?</h2> <p><strong>Use it with caution. The Wu-Xia shadow rate extends the federal funds series through the effective-lower-bound period, but it generates persistent price puzzles in modern-sample VARs and the resulting shocks transmit implausibly through money markets. Its sensitivity to minor modeling choices adds further reason for caution.</strong></p> <p><a href="https://doi.org/10.1111/jmcb.12300">Wu and Xia proposed the shadow rate to summarize the macroeconomic stance of policy during the effective-lower-bound period</a> , and it has been widely adopted. <a href="https://doi.org/10.1111/jmcb.12613">Krippner, however, demonstrates that shadow short-rate estimates are sensitive to minor estimation choices, and those sensitivities propagate into wide variations in inferred UMP effects</a> . <a href="https://doi.org/10.1111/jmcb.12522">Keating, Kelly, Smith and Valcarcel earlier showed that incidences of the price puzzle are exacerbated in SVARs that include various shadow interest rates for a modern sample</a> .</p> <p><a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021) find the shadow rate produces puzzling price responses across 23 specifications spanning 1988-2020, with the puzzle emerging as early as three months post-shock and persisting at 60-month horizons</a> . The responses for slices at December 2008, November 2010, and September 2012 — the starts of QE1, QE2, and QE3 — all show price puzzles for the Wu-Xia specification while the DM4 and DM2 specifications at the same dates show theory-consistent, quantitatively large price responses.</p> <p><strong>Practical guidance for a modern-sample VAR:</strong></p> <ol> <li>If you need a rate indicator, document the puzzle and treat the effective lower bound period as a structural break rather than a continuous series.</li> <li>Consider Divisia M4 as the policy indicator. The &ldquo;post-1984&rdquo; Great Moderation break in macro dynamics and the Monetary Control Act of 1980 are good reasons to begin samples in the late 1980s, where Divisia performs well.</li> <li>If you need an external instrument, <a href="https://doi.org/10.1016/j.jmoneco.2018.07.011">Arias, Caldara and Rubio-Ramírez&rsquo;s agnostic sign-restriction identification of the systematic component</a> offers an alternative to high-frequency surprise methods.</li> <li><a href="https://doi.org/10.18651/RWP2020-23">For event studies around quantitative tightening or balance-sheet normalization, Smith and Valcarcel demonstrate that short-rate indicators miss first-order financial-market effects that become visible through careful daily-frequency analysis</a> .</li> </ol> <hr> <h2 id="q6-what-is-the-divisia-monetary-aggregate-and-why-does-it-matter-for-monetary-policy-identification">Q6. What is the Divisia monetary aggregate and why does it matter for monetary policy identification?</h2> <p><strong>Divisia monetary aggregates, developed by William Barnett, weight each component of the money stock by its user cost — recognizing that currency, demand deposits, savings, money-market funds, and T-bills provide different flows of liquidity services and have different opportunity costs. Simple-sum aggregates (M1, M2) treat all components as perfect substitutes, which is both theoretically wrong and empirically disabling.</strong></p> <p>The theoretical case is the Barnett critique: simple-sum aggregates violate aggregation theory by adding assets that are not perfect substitutes. <a href="https://doi.org/10.1086/262052">Belongia showed empirically that replacing simple-sum with Divisia reverses the qualitative inference of four of five influential monetary studies</a> . <a href="https://doi.org/10.1016/j.jeconom.2014.06.006">Belongia and Ireland formalized the Barnett critique inside a New Keynesian model, demonstrating that a Divisia quantity tracks the theoretically correct monetary services aggregate almost perfectly while simple-sum does not</a> . <a href="https://doi.org/10.1080/07350015.2014.946132">They later showed that interest rates and Divisia money jointly provide the best measurement of monetary policy stance</a> .</p> <p><a href="https://doi.org/10.1016/j.jmacro.2019.103128">Belongia and Ireland also document a stable cointegrating money demand function for Divisia M2 and MZM over 1967-2019 — including the financial innovations of the 1980s and the post-2008 period — which undermines the long-standing claim that money demand is inherently unstable</a> .</p> <p>Chen and Valcarcel (2021) operationalize these insights for modern-sample monetary policy identification. <a href="https://doi.org/10.1016/j.jedc.2021.104214">They use the Center for Financial Stability&rsquo;s Divisia series at three levels of aggregation</a> : <strong>Divisia M1</strong> (currency, demand deposits, OCDs at banks and thrifts); <strong>Divisia M2</strong> (DM1 + savings deposits, retail money-market funds, small time deposits); and <strong>Divisia M4</strong> (DM2 + institutional money-market funds, large time deposits, repurchase agreements, commercial paper, and 3-month T-bills — 15 components total, the broadest U.S. monetary aggregate currently available).</p> <p><strong>Why Divisia M4 is the right choice for modern-sample VARs:</strong></p> <ol> <li>Its 15-component breadth captures the post-1980 financial ecosystem — repos, institutional money funds, commercial paper — that narrow aggregates miss.</li> <li>It properly weights each component by user cost, respecting the Barnett critique.</li> <li>In Chen-Valcarcel&rsquo;s block-recursive identification, it generates theory-consistent responses without commodity prices or futures data.</li> <li>It exhibits a stable cointegrating money demand relationship over the full modern period.</li> </ol> <hr> <h2 id="related-work">Related Work</h2> <p>This paper connects to Chen&rsquo;s broader research program on monetary policy identification. <a href="https://doi.org/10.1016/j.jmacro.2025.103736">Chen (2026, <em>Journal of Macroeconomics</em>)</a> extends the identification question to high-frequency monetary policy surprises, showing that the Fed responds primarily to financial conditions while adopting a &ldquo;wait-and-see&rdquo; stance on recent economic data. <a href="https://doi.org/10.1016/j.jedc.2024.104999">Chen (2025, <em>Journal of Economic Dynamics and Control</em>)</a> examines forward-looking monetary policy rules and their implications for inflation expectations.</p> <h2 id="data-and-replication">Data and Replication</h2> <p>All data and code for <a href="https://doi.org/10.1016/j.jedc.2021.104214">Chen and Valcarcel (2021)</a> are available at <a href="https://www.robinchen.org/">robinchen.org</a> . The paper uses:</p> <ul> <li><a href="https://centerforfinancialstability.org/amfm.php">Center for Financial Stability Divisia Monetary Aggregates</a> (monthly, M1/M2/M4)</li> <li>Wu-Xia shadow federal funds rate</li> <li>14 money-market component series (currency, demand deposits, OCDs, savings, IMMFs, LTDs, repos, CP, T-bills, and more)</li> <li>CRB and IMF commodity price indices</li> <li>30-day federal funds futures rate</li> </ul> <h2 id="citation">Citation</h2> <p>Chen, Zhengyang, and Victor J. Valcarcel. 2021. &ldquo;Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle.&rdquo; <em>Journal of Economic Dynamics and Control</em> 131: 104214. <a href="https://doi.org/10.1016/j.jedc.2021.104214">https://doi.org/10.1016/j.jedc.2021.104214</a> </p> <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-bibtex" data-lang="bibtex"><span class="line"><span class="cl"><span class="nc">@article</span><span class="p">{</span><span class="nl">chenvalcarcel2021</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">title</span><span class="p">=</span><span class="s">{Monetary Transmission in Money Markets: The Not-So-Elusive Missing Piece of the Puzzle}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">author</span><span class="p">=</span><span class="s">{Chen, Zhengyang and Valcarcel, Victor J.}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">journal</span><span class="p">=</span><span class="s">{Journal of Economic Dynamics and Control}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">volume</span><span class="p">=</span><span class="s">{131}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">pages</span><span class="p">=</span><span class="s">{104214}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">year</span><span class="p">=</span><span class="s">{2021}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">publisher</span><span class="p">=</span><span class="s">{Elsevier}</span><span class="p">,</span> </span></span><span class="line"><span class="cl"> <span class="na">doi</span><span class="p">=</span><span class="s">{10.1016/j.jedc.2021.104214}</span> </span></span><span class="line"><span class="cl"><span class="p">}</span> </span></span></code></pre></div>