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### I. INTRODUCTION
- Inventory behavior debated as either negligible or essential to understanding business cycles (Blinder, 1990, p. 74).
- Recent literature attributes part of the “Great Moderation” to inventory management improvements (Kim and Nelson, 1999; Blanchard and Simon, 2001; McConnell and Perez-Quirós, 2000; Kahn, McConnell, and Perez-Quirós, 2002).
- Inventory investment was a key contributor to the U.S. recovery around 2009–2010: “the biggest source of expansion in the second half of this year [2009 and the first quarter of 2010] is to come from a diminished pace of inventory liquidation by manufacturers, whole sellers, and retailers. Such a pattern is typical of business cycles. Inventory investment is often the catalyst for economic recoveries” (Yellen, 2009).
- Empirical notes:
  - In 2009 Q3 and Q4, the slowdown in inventory destocking contributed one-third and two-thirds of the overall quarter-on-quarter growth rate, respectively.
  - Some research suggests improved inventory management can weaken recoveries (Camacho, Perez-Quirós, and Rodriguez, 2009).
  - European upturns less pronounced than U.S. upturns; inventories’ role in large European economies not systematically analyzed prior to this paper.
- Paper scope:
  - Analyze inventory behavior in France, Germany, and Italy over the last 20 years.
  - Present stylized facts, scorecard of standard inventory models, inventories’ ability to foreshadow output growth, and implications of ignoring inventories in forecasts.
  - Sections II–III examine broader European evidence; Section IV concludes.

### II. INVENTORY BEHAVIOR — STYLIZED FACTS
- Long-run trends and averages:
  - Over the last twenty years, changes in inventories show no trend for the largest European economies except Germany (Figure 2).
  - France and Italy average changes in inventories: 0.1 percent of GDP and 0.2 percent of GDP, respectively.
  - France five-period averages (percent of GDP) for 1991–95, 1996–2000, 2001–05, and 2006–09: -0.2, 0.3, 0.3, and 0.0.
  - Italy comparable averages: 0.0, 0.4, 0.2, and 0.3.
  - United States: average changes in inventories 0.3 percent of GDP over full sample; period averages 0.3, 0.6, 0.2, and -0.1 for 1991–95, 1996–2000, 2001–05, and 2006–09.
  - Germany trend: average changes swung from 0.8 percent of GDP for 1991–2000 to -1.0 percent of GDP more recently.
  - Note on measurement: inventories for Eurostat countries computed as difference between gross capital investment and gross fixed capital investment; the United States reports inventories separately (see Appendix 1).
  - Decline in German inventories could reflect improved inventory management but persistence suggests inventory investment may act as a balancing item in national accounts.
- Cyclical behavior and contributions to recessions and recoveries:
  - Germany and Italy: average inventory contribution to growth was counter-cyclical (positive contribution in downswings; negative in upturns).
  - France: inventories behaved pro-cyclically in downswings but mostly counter-cyclically in upturns.
  - United States: inventories consistently behaved pro-cyclically in recent business cycles.
  - In all three recessions in the sample, inventory contribution to growth was negative and explained on average more than a third of the GDP decline.
  - In recent upswings, average inventory contribution was positive and accounted for nearly half of the GDP increase in these periods.
  - Timing in recoveries:
    - Inventories contributed to recoveries in France, Germany, and Italy with a roughly one-year delay.
    - Inventories placed a small drag on growth in first two quarters of recoveries in France and Italy; in Germany the initial drag was larger and lasted about twice as long.
    - Inventories boosted growth roughly a year into recovery in all three European countries.
    - Contrastingly, in the United States inventories supported upswings throughout the first 6 quarters of recovery, though the boost since 1991 was less pronounced than earlier cycles (Sichel, 1994).

### II. INVENTORY BEHAVIOR — HOW WELL DO SIMPLE INVENTORY MODELS FIT THE DATA?
- Volatility and correlations:
  - Across the sample, output volatility exceeds that of sales (sales = output minus inventories) in large European countries; this became more pronounced since 2008 (Table 2).
  - Filtered (Christiano-Fitzgerald band-pass) data for business cycle frequencies (six to 24 quarters) show similar patterns; at high frequency (three to six quarters), except for the United States, output variance is less than inventory variance.
  - Sales and changes in inventories co-move:
    - France and Italy: correlation positive and strengthened since 2008.
    - Germany and United States: historically negative correlation over the full sample but changed sign more recently.
- Model consistency — standard buffer-stock (demand-shock) model:
  - Predictions: sales more volatile than output; changes in inventories negatively correlated with sales.
  - Germany fully consistent with standard buffer-stock model (Table 3).
  - United States consistent for unfiltered data but not for business cycle or high-frequency movements.
  - Italy and France: standard model consistent only at high-frequency movements.
  - Support in filtered data may reflect higher-frequency movements driven by demand shocks.
- Model consistency — modified buffer-stock (supply shocks) and (S, s) rule:
  - Predictions: output more volatile than sales; changes in inventories positively correlated with sales.
  - France and Italy: predictions consistent (except at high-frequency movements).
  - Germany: not consistent with these predictions.
  - United States: only cyclical frequency behavior consistent with modified buffer-stock or (S, s).
- Cross-country and manufacturing sector patterns:
  - Economies with larger manufacturing sectors more likely characterized by production-smoothing and/or standard buffer-stock models; (S, s) rule likelier with smaller manufacturing sectors.
  - Bivariate regressions: larger (smaller) manufacturing sector associated with higher (lower) likelihood that volatility of sales exceeds that of output and stronger (weaker) negative correlation between sales and inventories; estimates not statistically significant and explain little cross-country variation.
  - Splitting sample into countries well characterized by standard buffer-stock model (Ireland, Germany, the Netherlands, United States) versus others increases explanatory power.

### BOX 1 — TWO SIMPLE MODELS OF INVENTORIES (MICRO FOUNDATIONS AND IMPLICATIONS)
- Two frameworks:
  - Production-smoothing/buffer-stock model: firms hold inventories to avoid production disruptions; marginal cost of inventories upward sloping.
  - (S, s) rule: fixed ordering cost plus constant marginal cost; firms reorder when inventories fall below s to restore to S; order size S-s.
- Key behavioral implications:
  - Standard buffer-stock (demand-shock) predictions:
    - Sales more volatile than output.
    - Firms meet unusually high demand by drawing down inventories, reducing output volatility.
    - Negative correlation between changes in inventories and sales.
  - Supply-shock scenario:
    - Firms observe unusually low marginal costs and boost production (and build inventories).
    - Output may be more volatile than sales; positive correlation between changes in inventories and sales.
  - (S, s) rule aggregate predictions resemble supply-shock predictions for volatility; correlation sign depends on initial inventories and shock history.
- Variance decomposition: Var(Y) = Var(S) + Var(ΔInv) + 2 Cov(S, ΔInv).
- Country classifications from empirical patterns:
  - Standard buffer-stock consistent: Ireland, Germany, the Netherlands, United States (with caveats).
  - Modified/nonstandard buffer-stock (supply-shock predominance): France, Italy, and several other European economies.
- Labor market rigidities:
  - Less flexible labor markets expected to damp output volatility by reducing labor input volatility.
  - Bivariate regressions alone not strongly supportive, but sample splits yield statistically significant estimates: greater labor market rigidities (OECD employment protection legislation index) accentuate stylized facts for standard buffer-stock countries with little effect on nonstandard buffer-stock countries.

### FORECASTING OUTPUT GROWTH — MODELS, EXPERIMENT DESIGN, AND RESULTS
- Forecasting frameworks:
  - Base AR model for output growth: ŷt = A(L) ŷt-1 + μ̂t; lag polynomial A(L) chosen to minimize Theil’s U-statistic at a four-quarter forecast horizon.
  - Augmented perfect-foresight model: ŷt = Ã(L) ŷt-1 + B(L) Δinv̂t-1 + μ̃t (forecasts conditional on future path of inventories; analyst has perfect foresight of inventories).
  - Augmented VAR (dynamic forecasting): Δinv̂t = C(L) Δinv̂t-1 + D(L) ŷt-1 + μ̃t (both variables dynamically forecasted).
- Thought experiment:
  - True DGP assumed bivariate VAR. Compare full augmented (VAR) forecasts to augmented forecasts where Δinv = 0 in the forecast horizon.
  - If true DGP is augmented VAR, setting Δinv = 0 should worsen forecast performance.
- Forecasting setup:
  - Horizons up to eight quarters.
  - Race from 2005:Q1 forecast using data through end-2004 continuing through 2009:Q4, yielding 20 forecasts at horizon one, 19 at horizon two, …, 13 at horizon eight.
  - Forecast error statistics computed for unfiltered, cyclical, and high-frequency components.
- Baseline performance (2005–09):
  - Base models over-shot growth on average in 2005–09.
    - Europe: about 10–15 basis points at horizon one to about 40–70 basis points at horizon eight.
    - United States: over-shooting larger at short horizons—about 30 basis points at horizon one—but comparable for horizons > three quarters.
  - Theil U-statistics < 1 indicate base models outperformed a naïve forecast in Germany and France, and to a lesser extent Italy and the United States.
- Impact of adding inventories:
  - Adding inventories improves forecasts mainly at horizons of four quarters or higher.
    - U-statistics decrease for both perfect foresight ("actual") and dynamically forecasted ("dynamic") inventory variants compared to base model at horizons ≥ four quarters (Table 6).
    - Italy: adding inventories improves growth forecasts for horizons ≤ four quarters.
    - Improvements concentrated in cyclical and high-frequency components rather than unfiltered growth.
    - Perfect foresight inventory models typically yield better forecasts than dynamically forecasted inventories.
- Effect of setting Δinv = 0 (ignoring inventory cycle):
  - Mixed consequences (Table 7):
    - Unfiltered data: output growth forecasts broadly improve in Europe (except horizons 4–6 in Germany); in United States forecasts worsen for horizons > three quarters.
    - Cyclical frequencies: forecasts improve for Italy, roughly unaffected in France, worsen in Germany; in United States forecasts worsen.
    - High frequencies: forecasts broadly worsen, with exception of horizons > six quarters in Italy; in United States impact alternates across horizons.
  - Overall implication: inventories help forecasting primarily at higher frequencies where demand shocks likely dominate.
- Country-level summary (UK and smaller European countries):
  - Base models over-shot growth during 2005–09 on average (about 10–20 basis points at horizon one to about 50–100 basis points at horizon eight; exceptions Ireland and Luxembourg had much higher errors).
  - Theil U-statistics < 1 for most countries except Spain.
  - Adding inventories produced mixed evidence: U-statistics often worsened but improved for Ireland and the Netherlands—countries best characterized by demand shocks.
  - Setting Δinv = 0 improved forecasts in most countries except Ireland and at longer horizons in the United Kingdom.
- Statistical testing and tables:
  - Modified Diebold-Mariano test (Harvey, Leybourne, and Newbold, 1997) used to compare mean squared prediction errors.
  - Tables A3a/A3b report ME, MAE, RMSE, U-stat across horizons and lag choices (examples: Austria lags=15; Belgium lags=16; Netherlands lags=5; Spain lags=1; UK lags=3).
  - Table A4a/A4b report augmented model performance with "actual" and "dynamic" inventory variants and one-sided p-values; significance noted at *, **, *** for 10 percent, 5 percent, 1 percent.
  - Table A5 reports Theil U-stat comparisons for Δinv = 0 experiments with p-values.

### INTERPRETATION AND POLICY-RELEVANT IMPLICATIONS
- Inventory cycles and recovery shape:
  - In Europe, inventories typically boosted recovery about a year into recoveries, implying U-shaped recoveries (recoveries take about a year to take hold).
  - In the United States, inventories have consistently contributed to growth in recoveries but less sharply than in prior cycles—V-shaped recovery pattern persists but the recovery leg is less pronounced.
- Implications for forecasting and policy:
  - Inventories provide limited but non-negligible information for forecasting output growth, most notably at horizons of four quarters or more and at higher frequencies.
  - Forecasting improvements more prevalent when standard buffer-stock (demand-shock) model characterizes inventory behavior (e.g., Ireland, Germany, the Netherlands).
  - Mechanisms for why inventories help when demand shocks prevail:
    - Demand shocks may have greater persistence (autocorrelation), so inventories anticipate future demand.
    - Labor market rigidities may damp output fluctuations and increase the information content of inventories.
  - Caveat: dynamically forecasting inventories can introduce volatility that detracts from output growth forecasts; in some settings, ignoring future evolution of inventories (setting Δinv = 0) improves forecast accuracy—suggesting inventories help mainly by improving estimates of output dynamics rather than by virtue of their own noisy evolution.
- Research priorities:
  - Need for direct evidence on dominance of specific shocks (demand versus supply).
  - Examine the distribution of shocks—a critical element for (S, s) rules and for understanding cross-country differences in inventory behavior.

### DATA, VALIDATION, AND ILLUSTRATIONS
- Sample and data sources:
  - Quarterly data from 1991:Q1 to 2009:Q4.
  - United States: Bureau of Economic Analysis (BEA).
  - Germany, France, Italy, and other European countries: Eurostat.
  - U.S. real changes in inventories reported separately; for Germany, France, Italy change in inventories computed as difference between real gross capital formation and real gross fixed capital formation (Appendix 1).
- Validation:
  - Comparison of residual-based inventory series and separately reported series for Spain, Belgium, and United States shows very small differences with correlations of 1.00 (Figure A1).
- Tables and figures:
  - Table A1: basic statistics (Var(GDP)/Var(sales), Correlation(sales, Δinv.)) for multiple countries with sample variations.
  - Table A2: Inventory Model Scorecard awarding up to five points per model criterion.
  - Figures A2–A5: country time series plots (unfiltered, cyclical, high-frequency) for Germany, France, Italy, United States with specified plot scales.

*Italic: Source: _wp10212 - References .............................................................................................................*

### References .............................................................................................................

### _wp10212 - References .............................................................................................................

### I. INTRODUCTION
- For decades economists and policy makers have debated inventory behavior’s role in the business cycle, ranging from “details of such little importance that economists could safely ignore” to “essential to achieving a better understanding not only of the macroeconomics of the business cycle but also of the microeconomics of the firm” (Blinder, 1990, p. 74).
- Recent literature attributes the “Great Moderation” to inventory management in addition to monetary policy improvements (Kim and Nelson, 1999; Blanchard and Simon, 2001; McConnell and Perez-Quirós, 2000; Kahn, McConnell, and Perez-Quirós, 2002).
- Inventory investment played a key role in the U.S. recovery around 2009–2010: “the biggest source of expansion in the second half of this year [2009 and the first quarter of 2010] is to come from a diminished pace of inventory liquidation by manufacturers, whole sellers, and retailers. Such a pattern is typical of business cycles. Inventory investment is often the catalyst for economic recoveries” (Yellen, 2009).
- In 2009 Q3 and Q4, the slowdown in inventory destocking contributed one-third and two-thirds of the overall quarter-on-quarter growth rate, respectively.
- Some research suggests improvements in inventory management may result in a weak U.S. recovery (Camacho, Perez-Quirós, and Rodriguez, 2009).
- European upturns have been less pronounced than U.S. upturns despite broad alignment; the role of inventories in European recoveries has not been systematically analyzed for large European economies (Cesaroni, Maccini, and Malgarini, 2009; Agresti and Mojon, 2001).
- This paper analyzes inventory behavior in France, Germany, and Italy over the last 20 years, presenting stylized facts, a scorecard of standard inventory models, inventories’ ability to foreshadow output growth, and implications of ignoring inventories in forecasts. Sections II–III examine broader European evidence; Section IV concludes.

### II. INVENTORY BEHAVIOR
#### A. Stylized Facts
- Over the last twenty years, changes in inventories have not exhibited a trend in the largest European economies except Germany (Figure 2).
- France and Italy average changes in inventories: 0.1 percent of GDP and 0.2 percent of GDP, respectively, with averages stable for the most part.
- France: average changes in inventories (as percent of GDP) for the five periods comprising 1991–95, 1996–2000, 2001–05, and 2006–09 are -0.2, 0.3, 0.3, and 0.0.
- Italy: comparable averages are 0.0, 0.4, 0.2, and 0.3.
- United States: changes in inventories have been higher and less stable, averaging 0.3 percent of GDP over the full sample; period averages are 0.3, 0.6, 0.2, and -0.1 for 1991–95, 1996–2000, 2001–05, and 2006–09.
- Germany exhibits a pronounced trend: average changes swung from 0.8 percent of GDP for 1991–2000 to -1.0 percent of GDP more recently.
- Note: inventories are computed as the difference between gross capital investment and gross fixed capital investment for Eurostat data, except the United States reports inventories separately (see Appendix 1).
- The implied decline in the level of German inventories could be consistent with improved inventory management, but persistence suggests inventory investment in Germany serves as a balancing item in national accounts.
- Inventory cyclical behavior:
  - In Germany and Italy, average contribution to growth from inventories has been counter-cyclical: in downswings (peak to trough) average contribution positive; in upturns (trough to following two quarters) average contribution negative (Table 1).
  - France: inventories behaved pro-cyclically in downswings but mostly counter-cyclically in upswings.
  - United States: inventories consistently behaved pro-cyclically in recent business cycles.
- In all three recessions in the sample, the inventory contribution to growth was negative and explained on average more than a third of the GDP decline.
- In recent upswings the average inventory contribution was positive and accounted for nearly half of the GDP increase in these periods.
- With a one-year delay, inventories have contributed to recent recoveries in France, Germany, and Italy (Figure 3):
  - Inventories placed a small drag on growth in the first two quarters of recoveries in France and Italy.
  - In Germany the initial drag was more notable and lasted twice as long.
  - Inventories boosted growth roughly a year into a recovery in all three European countries.
  - In contrast, inventories consistently supported U.S. upswings throughout the first 6 quarters of recovery, though the boost since 1991 has been less pronounced than earlier business cycles (Sichel, 1994).

#### B. How Well Do Simple Inventory Models Fit the Data?
- Over the sample, output volatility exceeds that of sales (sales defined as output minus inventories) in the large European countries; this pattern became more pronounced since 2008 (Table 2).
- Filtered data (Christiano-Fitzgerald band-pass filter) examining business cycle frequencies (six to 24 quarters) show a similar pattern. At high frequency (three to six quarters), except for the United States, output variance is less than inventory variance.
- Sales co-move with changes in inventories:
  - France and Italy: correlation of sales and changes in inventories is positive and strengthened since 2008.
  - Germany and the United States: correlation historically negative for the whole sample but changed sign in the more recent period.
  - These correlations behave similarly in filtered data.
- Standard buffer-stock model implications:
  - If firms hold inventories as a buffer, higher-than-anticipated demand is met by running down inventories, so output volatility would be lower than sales volatility and changes in inventories negatively correlated with sales.
  - Germany fully consistent with standard buffer-stock model (Table 3).
  - United States consistent for unfiltered data but not for business cycle or high-frequency movements.
  - Italy and France: standard model consistent only at high-frequency movements.
  - Support for standard buffer-stock model in filtered data may reflect higher-frequency movements driven by demand shocks.
- Modified buffer-stock model or (S, s) rule:
  - If supply (cost) shocks prevail and firms observe these before setting production, buffer-stock predicts output more volatile than sales and changes in inventories positively correlated with sales. (S, s) rule yields similar predictions.
  - These predictions are consistent with France and Italy (except high-frequency movements), but not with Germany.
  - United States: only cyclical frequency behavior consistent with modified buffer-stock or (S, s).
- United Kingdom and smaller European countries:
  - Modified buffer-stock model or (S, s) rule better describe the data: relative volatility of output to sales exceeds one and positive correlation of sales and changes in inventories in most countries (Tables A1 and A2).
  - Exceptions: Ireland and the Netherlands exhibit high sales volatility and inverse correlation of sales and changes in inventories, fully consistent with standard buffer-stock model.
- Cross-country patterns and manufacturing:
  - Cost structures imply economies with large manufacturing sectors more likely characterized by production-smoothing and/or standard buffer-stock models; (S, s) rule likelier in economies with smaller manufacturing sectors.
  - Bivariate regression shows the larger (smaller) the manufacturing sector, the more (less) likely the volatility of sales exceeds that of output and the stronger (weaker) the negative correlation between sales and inventories; however estimates are not statistically significant and explain little of cross-country variation.
  - Splitting the sample between countries well characterized by standard buffer-stock model (Ireland, Germany, the Netherlands, United States) and those that are not substantially increases explanatory power.

*Italic: Source: _wp10212 - References .............................................................................................................*

### Box 1. Two Simple Models of Inventories

### Box 1. Two Simple Models of Inventories

### Microeconomic frameworks and model mechanics
- Two simple microeconomic frameworks underlie inventory behavior:
  - A production-smoothing/buffer-stock model: firms hold stocks of inputs and/or finished goods to avoid production disruptions or stock-outs; the marginal cost (of inventories) is upward sloping.
  - An (S, s) rule (inspired by retail sales): inventory cost comprises a fixed cost of placing an order and a constant marginal cost per item. Firms choose an optimum s such that whenever inventories fall below s an order restores inventories to S; the optimum order size is S-s.
- Key behavioral implications:
  - Under a standard buffer-stock (demand-shock) model:
    - Sales are more volatile than output in the presence of demand shocks.
    - Profit-maximizing firms facing increasing marginal costs and uncertain demand meet unusually high demand by drawing down inventories rather than boosting production.
    - This reduces output volatility and results in a negative correlation between changes in inventories and sales.
  - Under supply shocks:
    - Firms observe unusually low marginal costs and choose to boost production (and build inventories).
    - Output may be more volatile than sales and the correlation between changes in inventories and sales is positive.
  - Under an (S, s) rule:
    - Predictions resemble those of supply shocks in aggregate (output volatility higher than sales), but the correlation between change in inventories and sales depends on the distribution of initial inventories and the history of shocks (how far inventories are from s).
    - If initially inventories are low, the correlation between the change in inventories and sales will be positive; otherwise the correlation will be small (or zero if no firm hits s).
- Variance decomposition formula (aggregate identity):
  - Var(Y) = Var(S) + Var(ΔInv) + 2 Cov(S, ΔInv).

### Empirical patterns and cross-country characterization
- General patterns and country classifications:
  - Inventory behavior consistent with a standard buffer-stock (demand-shock driven) model: Ireland, Germany, the Netherlands, and the United States (with caveats for the U.S. at business cycle and high-frequency movements).
  - A modified/nonstandard buffer-stock model (supply-shock predominance) better characterizes France, Italy, and a number of other European economies: predicts output volatility greater than sales and a positive correlation between changes in inventories and sales.
  - Differences in inventory behavior across Europe appear rooted in the nature of shocks—with supply shocks prevailing in most countries—rather than differences in the governing behavioral model.
  - The relation between the size of manufacturing and inventory stylized facts does not sit well with an (S, s) rule in several cases.
- Role of labor market rigidities:
  - Less flexible labor markets are expected to dampen output volatility by reducing labor input volatility.
  - Empirical evidence: a simple bivariate regression did not uncover strong evidence alone, but splitting the sample increases explanatory power and yields statistically significant estimates (column references in source). Greater labor market rigidities—measured using the OECD’s employment protection legislation index—accentuate the basic stylized facts for standard buffer-stock countries with little or no effect on nonstandard buffer-stock countries.

### Forecasting output growth: models and experiment design
- Baseline and augmented time-series frameworks:
  - Base model: an autoregressive (AR) model for output growth:
    - ŷt = A(L) ŷt-1 + μ̂t (lag polynomial A(L) chosen to minimize Theil’s U-statistic at a four-quarter forecast horizon; p selected accordingly).
  - Augmented model (perfect foresight version):
    - ŷt = Ã(L) ŷt-1 + B(L) Δinv̂t-1 + μ̃t (output growth forecasts conditional on the future path of inventories; analyst has perfect foresight regarding this path).
  - Augmented VAR (dynamic forecasting) version:
    - Δinv̂t = C(L) Δinv̂t-1 + D(L) ŷt-1 + μ̃t (both variables dynamically forecasted; amounts to a VAR).
- Thought experiment / horse race:
  - Assume the true DGP is the bivariate VAR. Compare:
    - Full augmented (VAR) forecasts (dynamic forecasting of inventories) and augmented forecasts where the change in inventories is set to zero in the forecast horizon (Δinv = 0).
  - If the true DGP is the augmented (VAR) model, disregarding the inventory cycle (setting Δinv = 0) should worsen forecast performance.

### Forecasting results and informational content of inventories
- Forecasting setup:
  - Forecast horizons up to eight quarters.
  - Race begins with forecast for 2005:Q1 using data through end-2004 and continues through 2009:Q4, yielding 20 forecasts at horizon one, 19 at horizon two, …, 13 at horizon eight.
  - Forecast error statistics computed for unfiltered data and for cyclical and high-frequency components.
- Baseline performance (summary):
  - On average, base models over-shot growth during 2005–09.
    - In Europe: about 10–15 basis points at horizon one quarter to about 40–70 basis points at horizon eight quarters.
    - In the United States: over-shooting larger at short horizons—about 30 basis points at horizon one quarter—but comparable for horizons greater than three quarters.
  - Theil U-statistics less than one indicate base models outperformed a naïve forecast (no change) in Germany and France, and to a lesser extent Italy and the United States.
- Adding inventories improves forecasts mainly at horizons of four quarters or higher:
  - U-statistics decrease for both the perfect foresight ("actual") and dynamically forecasted ("dynamic") changes in inventories compared to the base model at horizons of four quarters and beyond (Table 6 in source).
  - In Italy, adding inventories improves growth forecasts for horizons of four quarters or less.
  - Improvements are concentrated in cyclical and high-frequency components rather than unfiltered growth; at cyclical frequencies in France, inventories improve forecasts for horizons of four quarters or less.
  - Perfect foresight inventory models typically yield better forecasts than dynamically forecasted inventories.
- Setting changes in inventories to zero (Δinv = 0) has mixed consequences (Table 7):
  - For unfiltered data, output growth forecasts broadly improve in Europe (except horizons between four and six quarters in Germany); in the United States, forecasts worsen for horizons greater than three quarters.
  - For cyclical frequencies: forecasts improve for Italy, are roughly unaffected in France, and worsen in Germany; in the United States forecasts worsen.
  - For high frequencies: forecasts broadly worsen, with the exception of horizons greater than six quarters in Italy; in the United States the impact alternates over various horizons.
  - Overall implication: inventories help forecasting primarily at higher frequencies where demand shocks are more likely to dominate.
- Country-level summary for UK and smaller European countries:
  - Base models over-shot growth during 2005–09 on average (about 10–20 basis points at horizon one to about 50–100 basis points at horizon eight, with exceptions such as Ireland and Luxembourg which had much higher errors).
  - Theil U-statistics < 1 for most countries (base model outperformed naïve forecast) except Spain.
  - Adding inventories produced mixed evidence: U-statistics often worsened but improved for Ireland and the Netherlands—countries best characterized by demand shocks.
  - Setting Δinv = 0 improved forecasts in most countries except Ireland and at longer horizons in the United Kingdom.

### Interpretation and policy-relevant implications
- Inventory cycles and recoveries:
  - In Europe, inventories have contributed to recoveries with a lag over the past 20 years; in the three largest European economies inventories typically boosted recovery about a year into the recovery, implying U-shaped recoveries (recoveries take about a year to take hold).
  - In the United States, inventories have consistently contributed to growth in recoveries but less sharply than in prior cycles—V-shaped recovery pattern persists but the recovery leg is less pronounced.
- What models imply for forecasting and policy:
  - Inventories provide limited but non-negligible information for forecasting output growth, with the most noticeable improvements at forecast horizons of four quarters or more and at higher frequencies.
  - Improvements in forecasting growth are more prevalent when a standard buffer-stock (demand-shock) model best characterizes inventory behavior (e.g., Ireland, Germany, the Netherlands).
  - Possible mechanisms for why inventories help when demand shocks prevail:
    - Demand shocks may have greater persistence (autocorrelation), so inventories anticipate future demand.
    - Labor market rigidities may damp output fluctuations and increase the information content of inventories.
  - However, forecasting inventories dynamically can introduce volatility that detracts from output growth forecasts; in some settings, ignoring the future evolution of inventories (setting Δinv = 0) improves forecast accuracy—suggesting that inventories primarily help by improving estimates of output growth dynamics rather than by their own noisy evolution.
- Research priorities:
  - Further research is needed to provide direct evidence on the dominance of specific shocks (demand versus supply) and to examine the distribution of shocks—a critical element for (S, s) rules and for understanding cross-country differences in inventory behavior.

*Source: Box 1 and associated sections in the supplied IMF working-paper content.*

### REFERENCES

### REFERENCES

### Citations and Literature
- Extensive list of references cited in the paper, including but not limited to:
  - Agresti, Anna María, and Benoît Mojon, 2001.
  - Baxter, Marianne, and Robert G. King, 1999.
  - Blanchard, Olivier, 1983; Blanchard and John Simon, 2001.
  - Blinder, Alan S., 1990; Blinder and Louis J. Maccini, 1991.
  - Camacho, Máximo, Gabriel Perez-Quirós, and Hugo Rodriguez, 2009.
  - Cesaroni, Tatiana, Louis Maccini, and Marco Malgarini, 2009.
  - Christiano, Lawrence J. and Terry J. Fitzgerald, 2003.
  - Clarida, Richard, Jordi Galí, and Mark Gertler, 2000.
  - Diebold, Francis X., 2007.
  - Eichenbaum, Martin, 1984.
  - Harvey, David, Stephen Leybourne, and Paul Newbold, 1997.
  - Hornstein, Andreas, 1998.
  - Kahn, James, Margaret McConnell, and Gabriel Perez-Quirós, 2002.
  - Khan, Aubhik, and Julia K. Thomas, 2007.
  - Kim, Chang-Jin, and Charles Nelson, 1991.
  - Krugman, Paul, 2009.
  - Kryvtsov, Oleksiy, and Virgiliu Midrigan, 2009.
  - Menuet, Guillaume, 2009.
  - Sichel, Daniel E., 1994.
  - Yellen, Janet L., 2009.

### Methodological and Theoretical Sources
- References include methodology on band-pass filters, AR models, Markov-switching models, (S, s) inventory policies, inventory theory, and tests comparing mean squared prediction errors.
- Specific methodological citation: Harvey, Leybourne, and Newbold, 1997 (modified Diebold-Mariano test).

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### APPENDIX 1: DATA

### Sample and Sources
- Quarterly data from 1991:Q1 to 2009:Q4.
- United States data: Bureau of Economic Analysis (BEA).
- Germany, France, Italy, and other European country data: Eurostat.
- For the United States, real changes in inventories are reported separately.
- For Germany, France, and Italy, change in inventories is calculated as the difference between real gross capital formation and real gross fixed capital formation.

### Validation of Inventory Series
- Comparison performed between inventory series calculated as a residual and those reported separately for Spain, Belgium, and the United States.
- The differences between the two calculation methods in these three countries appear very small and the correlations are 1.00 (Figure A1).

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### TABLES: BASIC STATISTICS AND SCORECARDS

### Table A1. Basic Statistics (selected entries)
- Variables and sample periods reported (91:1 - 09:4 or 08:1 - 09:4).
- Examples of reported statistics:
  - Austria: Var (GDP) / var (sales) = 1.04; Correlation (sales, ∆inv.) = 0.53 (for 91:1 - 09:4) and 0.50 (for 08:1 - 09:4).
  - Belgium: Var (GDP) / var (sales) = 1.03; Correlation (sales, ∆inv.) = 0.25 and 0.87.
  - Ireland: Var (GDP) / var (sales) = 0.99; Correlation (sales, ∆inv.) = 1.66 and -0.08 and 0.90 (note: sample begins in 1991Q1).
  - Netherlands: Var (GDP) / var (sales) = 0.97; Correlation (sales, ∆inv.) = 1.39 and -0.35 and 0.65.
  - Spain: Var (GDP) / var (sales) = 1.01; Correlation (sales, ∆inv.) = 0.98 and 0.40 and -0.46.
- Notes:
  - All variables are in levels and constant prices.
  - Sales = GDP - change in inventories.
  - Some samples start in 1995Q1 for certain countries.

### Table A2. Inventory Model Scorecard (summary)
- Scorecard awards five points when the model's prediction is found in the data (authors' calculations based on Table A1).
- Models evaluated: Smoothing motive (demand shocks), Supply shocks, (S, s) model.
- Example cell interpretations (selected):
  - Austria: received "0" in Smoothing motive, "5" in Supply shocks, "5" in (S, s) model for Var (GDP)/var(sales) > 1 and Correlation (sales, ?inventories) > 0 criteria in certain subperiods.
  - Belgium, Netherlands, Spain, Portugal, UK show varying point allocations across the three model categories.

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### FORECASTING PERFORMANCE AND INVENTORY INFORMATION CONTENT

### Forecasting Framework and Metrics
- Forecast horizons reported from 1 to 8 quarters.
- Forecast performance metrics:
  - ME (mean error), MAE (absolute mean error), RMSE (root mean square error) measured in percentage points.
  - U-stat (Theil U-stat) is unitless.
- Baseline forecasting period: 2005:Q1 through 2009:Q2 (Tables A3a, A3b).
- Baseline model: individual country univariate AR models for output growth with lags selected to minimize the Theil U-stat at four quarters in the forecast period.

### Table A3a / A3b: Baseline Forecasting Performance (selected entries)
- Unfiltered series, various lags specified per country (examples):
  - Austria (lags=15): at horizon 1: ME = -0.02; MAE = 0.51; RMSE = 0.80; U-stat = 1.23; obs = 20.
  - Belgium (lags=16): at horizon 1: ME = -0.24; MAE = 0.49; RMSE = 0.83; U-stat = 1.24; obs = 20.
  - Netherlands (lags=5): at horizon 1: ME = -0.12; MAE = 0.62; RMSE = 0.87; U-stat = 0.93; obs = 20.
  - Spain (lags=1): at horizon 1: ME = -0.17; MAE = 0.49; RMSE = 0.75; U-stat = 1.14; obs = 20.
  - UK (lags=3): at horizon 1: ME = -0.15; MAE = 0.60; RMSE = 0.81; U-stat = 1.04; obs = 20.

### Table A4a / A4b: Assessing the Information Content of Inventories in Forecasting Output Growth
- Augmented models include corresponding lags in the "growth" of the change in inventories.
- Two forecast variants:
  - "actual": assume perfect inventory foresight in the forecast horizon.
  - "dynamic": forecast inventories dynamically using a bivariate VAR model.
- P-values correspond to a one-sided t-test comparing mean square errors of the base model to the augmented models (modified Diebold-Mariano test).
- Significance notation: * (10 percent), ** (5 percent), *** (1 percent).
- Selected entries:
  - Austria (Unfiltered): horizon 1: Base model Theil U-stat = 1.230; Augmented (actual) = 1.938; p-value = 0.01 ***.
  - Belgium (Unfiltered): horizon 1: Base model = 1.244; Augmented (actual) = 3.617; p-value = 0.06 *.
  - Ireland (Unfiltered): horizon 1: Base model = 0.815; Augmented (actual) = 0.715; p-value = 0.02 **.
  - Luxembourg (Unfiltered): horizon 1: Base model = 0.978; Augmented (actual) = 0.984; p-value = 0.220.
  - Netherlands, Spain, Portugal, UK: tables report base vs. augmented Theil U-stats across horizons with p-values and lag selections per country.

### Table A5: Effect of Setting Inventory Forecasts to Zero
- Bivariate VAR models for output growth and "growth" in the change in inventories used; lags selected using same criteria as Table 4.
- The U-stat for ∆inv=0 corresponds to forecasts when the "growth" in the change in inventories is set to zero in the forecast period.
- P-values compare MSE of the two model forecasts (modified Diebold-Mariano test).
- Selected entries (Theil U-stat comparisons):
  - Austria (lags=12): horizon 1: Unfiltered = 1.255; Augmented = 1.019; p-value = 0.02 **.
  - Belgium (lags=2): horizon 1: Unfiltered = 7.434; Augmented = 1.175; p-value = 0.22.
  - Ireland (lags=3): horizon 1: Unfiltered = 0.721; Augmented = 0.827; p-value = 0.02 **.
  - Luxembourg (lags=1): horizon 1: Unfiltered = 0.979; Augmented = 1.016; p-value = 0.05 **.
  - Additional country-specific results for horizons 1–8 reported with p-values and Theil U-statistics.

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### FIGURES AND ILLUSTRATIONS

### Inventory Calculations and Comparisons
- Figure A1: Calculations of Inventories — Real Changes in Inventories plotted for 1995Q1 through 2009Q1:
  - Spain: inventories as residual (left scale) and Chg in Bus Inv/Acq less Disposals (SWDA, Mil.Ch.00.EUR).
  - Belgium: inventories as residual (left scale) and Changes in Inventories (SWDA, Mil.Ch.00.EUR).
  - US: change in inventories as residual (right scale) and US Real Change in Private Inventories (SAAR, Bil.Chn.2005$).
  - Visual scales shown with values ranging between -1,000 and 1,500 (left) and -200 to 150 (right) per plotted series.

### Country Time Series Plots (1991Q1 - 2009Q4)
- Figure A2. Germany: GDP, Sales, Changes in Inventories (constant prices, million euros). Panels include:
  - Unfiltered series (Change in GDP, Change in sales, Change in inventories) with scale -25,000 to 25,000.
  - Cyclical components (YCYC, SALESCYC, INVCYC) with scale -20,000 to 20,000.
  - High frequency components (YHF, SALESHF, INVHF) with scale -8,000 to 6,000.
- Figure A3. France: GDP, Sales, Changes in Inventories (constant prices, million euros). Panels include:
  - Unfiltered series with scale -8,000 to 8,000.
  - Cyclical components with scale -8,000 to 8,000.
  - High frequency components with scale -2,500 to 2,500.
- Figure A4. Italy: GDP, Sales, Changes in Inventories (constant prices, million euros). Panels include:
  - Unfiltered series with scale -12,000 to 8,000.
  - Cyclical components with scale -10,000 to 8,000.
  - High frequency components with scale -4,000 to 3,000.
- Figure A5. United States: GDP, Sales, Changes in Inventories, 1991Q1-2009Q4 (constant prices, billion US dollars). Panels include:
  - Unfiltered series with scale -250 to 250 for change in GDP, and -300 to 250 for cyclical components.
  - High frequency components with scale -80 to 80.

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*Source: _wp10212 - REFERENCES (Appendix and Figures).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10212.pdf_