Saeed Zaman

This paper examines the predictive relationship between the distribution of realized inflation in the US and measures of inflation expectations from households, firms, financial markets, and professional forecasters. To allow for nonlinearities in the predictive relationship we use quantile regression methods. We find that the ability of households to predict future inflation, relative to that of professionals, firms, and the market, increases with inflation. While professional forecasters are more accurate in the middle of the inflation density, households’ expectations are more useful in the upper tail. The predictive ability of measures of inflation expectations is greatest when combined. We show that it is helpful to let the combination weights on different agents’ expectations of inflation vary by quantile when assessing inflationary pressures probabilistically.

We implement a novel nonlinear structural model featuring an empirically-successful frequency-dependent and asymmetric Phillips curve; unemployment frequency components interact with three components of core PCE – core goods, housing, and core services ex-housing – and a variable capturing supply shocks. Forecast tests verify model’s accuracy in its unemployment-inflation tradeoffs, crucial for monetary policy. Using this model, we assess the plausibility of the December 2022 Summary of Economic Projections (SEP). By 2025Q4, the SEP projects 2.1 percent inflation; however, conditional on the SEP unemployment path, we project inflation of 2.9 percent. A fairly deep recession delivers the SEP inflation path, but a simple welfare analysis rejects this outcome.

Theory and extant empirical evidence suggest that the cross-sectional asymmetry across disaggregated price indexes might be useful in forecasting aggregate inflation. Trimmed-mean inflation estimators have been shown to be useful devices for forecasting headline PCE inflation. But is this because they signal the underlying trend or because they implicitly signal asymmetry in the underlying distribution? We address this question by augmenting a "hard" to beat benchmark headline PCE inflation forecasting model with robust trimmed-mean inflation measures and robust measures of the cross-sectional skewness, both computed using the 180+ components of the PCE price index. Our results indicate significant gains in the point and density accuracy of PCE inflation forecasts over medium- and longer-term horizons, up through and including the COVID-19 pandemic. Improvements in accuracy stem mainly from the trend information implicit in trimmed-mean estimators, but skewness information is also useful. An examination of goods and services PCE inflation provides similar inference.

In the December 2022 Summary of Economic Projections (SEP), the median projection for four-quarter core PCE inflation in the fourth quarter of 2025 is 2.1 percent. This same SEP has unemployment rising by nine-tenths, to 4.6 percent, by the end of 2023. We assess the plausibility of this projection using a specific nonlinear model that embeds an empirically successful nonlinear Phillips curve specification into a structural model, identifying it via an underutilized data-dependent method. We model core PCE inflation using three components that align with those noted by Chair Powell in his December 14, 2022, press conference: housing, core goods, and core-services-less-housing. Our model projects that conditional on the SEP unemployment rate path and a rapid deceleration of core goods prices, core PCE inflation moderates to only 2.75 percent by the end of 2025: inflation will be higher for longer. A deep recession would be necessary to achieve the SEP’s projected inflation path. A simple reduced-form welfare analysis, which abstracts from any danger of inflation expectations becoming unanchored, suggests that such a recession would not be optimal.

What drove inflation so high in 2022? Can it drop rapidly without a recession? The Phillips curve is central to the answers; its proper (nonlinear) specification reveals that the relationship is strong and frequency dependent, and inflation is very persistent. We embed this empirically successful Phillips curve – incorporating a supply-shocks variable – into a structural model. Identification is achieved using an underutilized data-dependent method. Despite imposing anchored inflation expectations and a rapid relaxation of supply-chain problems, we find that absent a recession, inflation will be more than 3 percent by the end of 2025. A simple welfare analysis supports a mild recession as preferred to an extended period of elevated inflation, under a typical loss function.

We develop a flexible semi-structural time-series model to estimate jointly several macroeconomic "stars" -- i.e., unobserved long-run equilibrium levels of output (and growth rate of output), the unemployment rate, the real rate of interest, productivity growth, price inflation, and wage inflation. The ingredients of the model are in part motivated by economic theory and in part by the empirical features necessitated by the changing economic environment. Following the recent literature on inflation and interest rate modeling, we explicitly model the links between long-run survey expectations and stars to improve the stars' econometric estimation. Our approach permits time variation in the relationships between various components, including time variation in error variances. To tractably estimate the large multivariate model, we use a recently developed precision sampler that relies on Bayesian methods. The by-products of this approach are the time-varying estimates of the wage and price Phillips curves, and the pass-through between prices and wages, both of which provide new insights into these empirical relationships' instability in US data. Generally, the contours of the stars echo those documented elsewhere in the literature -- estimated using smaller models -- but at times the estimates of stars are different, and these differences can matter for policy. Furthermore, our estimates of the stars are among the most precise. Last, we document the competitive real-time forecasting properties of the model and, separately, the usefulness of stars' estimates as steady-state values in external models.

Both theory and extant empirical evidence suggest that the cross-sectional asymmetry across disaggregated price indexes might be useful in the forecasting of aggregate inflation. Trimmed-mean inflation estimators have been shown to be useful devices for forecasting headline PCE inflation. But does this stem from their ability to signal the underlying trend, or does it mainly come from their implicit signaling of asymmetry (when included alongside headline PCE)? We address this question by augmenting a “hard to beat” benchmark inflation forecasting model of headline PCE price inflation with robust measures of trimmed-mean estimators of inflation (median PCE and trimmed-mean PCE) and robust measures of the cross-sectional asymmetry (Bowley skewness; Kelly skewness) computed using the 180+ components of the PCE price index. We also construct new trimmed-mean measures of goods and services PCE inflation and their accompanying robust skewness. Our results indicate significant gains in the point and density accuracy of PCE inflation forecasts over medium- and longer-term horizons, up through and including the COVID-19 pandemic. We find that improvements in accuracy stem mainly from the trend information implicit in trimmed-mean estimators, but that skewness is also useful. Median PCE slightly outperforms trimmed-mean PCE; both outperform core PCE. For point forecasts, Kelly skewness is preferred; but for estimating stochastic volatility, Bowley skewness is preferred. An examination of goods and services PCE inflation provides similar inference.

We develop a flexible semi-structural time-series model to estimate jointly several macroeconomic "stars" — i.e., unobserved long-run equilibrium levels of output (and growth rate of output), the unemployment rate, the real rate of interest, productivity growth, the price inflation, and wage inflation. The ingredients of the model are in part motivated by economic theory and in part by the empirical features necessitated by the changing economic environment. Following the recent literature on inflation and interest rate modeling, we explicitly model the links between long-run survey expectations and stars to improve the stars' econometric estimation. Our approach permits time variation in the relationships between various components, including time variation in error variances. To tractably estimate the large multivariate model, we use a recently developed precision sampler that relies on Bayesian methods. The by-products of this approach are the time-varying estimates of the wage and price Phillips curves, and the pass-through between prices and wages, both of which provide new insights into these empirical relationships' instability in US data. Generally, the contours of the stars echo those documented elsewhere in the literature — estimated using smaller models — but at times the estimates of stars are different, and these differences can matter for policy. Furthermore, our estimates of the stars are among the most precise. Lastly, we document the competitive real-time forecasting properties of the model and, separately, the usefulness of stars' estimates if they were used as steady-state values in external models.

We develop a flexible modeling framework to produce density nowcasts for US inflation at a trading-day frequency. Our framework: (1) combines individual density nowcasts from three classes of parsimonious mixed-frequency models; (2) adopts a novel flexible treatment in the use of the aggregation function; and (3) permits dynamic model averaging via the use of weights that are updated based on learning from past performance. Together these features provide density nowcasts that can accommodate non-Gaussian properties. We document the competitive properties of the nowcasts generated from our framework using high-frequency real-time data over the period 2000-2015.

We document asymmetric responses of consumer spending to energy price shocks: Using a multiple-regime threshold vector autoregressive model estimated with Bayesian methods on US data, we find that positive energy price shocks have a larger negative effect on consumption compared with the increase in consumption in response to negative energy price shocks. For large shocks, the cumulative consumption responses are three to five times larger for positive than for negative shocks. Digging into disaggregated spending, we find that the estimated asymmetric responses are strongest for durable goods, but asymmetries are also present in the responses of nondurables and services.

This paper constructs hybrid forecasts that combine both short- and long-term conditioning information from external surveys with forecasts from a standard fixed-coefficient vector autoregression (VAR) model. Specifically, we use relative entropy to tilt one-step ahead and long-horizon VAR forecasts to match the nowcast and long-horizon forecast from the Survey of Professional Forecasters. The results indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. The accuracy gains are achieved for a range of variables, including those that are not directly tilted but are affected through spillover effects from tilted variables. The forecast accuracy gains for inflation are substantial, statistically significant, and are competitive with the forecast accuracy from both time-varying VARs and univariate benchmarks. We view our proposal as an indirect approach to accommodating structural change and moving end points.

Financial data often contain information that is helpful for macroeconomic forecasting, while multistep forecast accuracy also benefits by incorporating good nowcasts of macroeconomic variables. This paper considers the role of nowcasts of financial variables in making conditional forecasts of real and nominal macroeconomic variables using standard quarterly Bayesian vector autoregressions (BVARs). For nowcasting the quarterly value of a variety of financial variables, we document that the average of the available daily data and a daily random walk forecast to fill in the missing days in the quarter typically outperforms other nowcasting approaches. Using real-time data and out-of-sample forecasting exercises, we find that the inclusion of financial variable nowcasts by themselves generally improves forecast accuracy for macroeconomic variables relative to unconditional forecasts, although we document several exceptions in which current-quarter forecast accuracy worsens with the inclusion of the financial nowcasts. Incorporating financial nowcasts and nowcasts of macroeconomic variables generally improves the forecast accuracy for all the macroeconomic indicators of interest, beyond including the nowcasts of the macroeconomic variables alone. Conditional forecasts generated from quarterly BVARs augmented with nowcasts of key financial variables rival the forecast accuracy of mixed-frequency dynamic factor models (MF-DFMs) and mixed-data sampling (MIDAS) models that explicitly link the quarterly data and forecasts to high-frequency financial data.

In this paper we investigate the forecasting performance of the median consumer price index (CPI) in a variety of Bayesian vector autoregressions (BVARs) that are often used for monetary policy. Until now, the use of trimmed-mean price statistics in forecasting inflation has often been relegated to simple univariate or "Phillips-curve" approaches, thus limiting their usefulness in applications that require consistent forecasts of multiple macro variables. We find that inclusion of an extreme trimmed-mean measure—the median CPI—improves the forecasts of both core and headline inflation (CPI and PCE) across our set of monthly and quarterly BVARs. While the inflation forecasting improvements are perhaps not surprising given the current literature on core inflation statistics, we also find that inclusion of the median CPI improves the forecasting accuracy of the central bank's primary instrument for monetary policy—the federal funds rate. We conclude with a few illustrative exercises that highlight the usefulness of using the median CPI.

We estimate an empirical model of inflation that exploits a Phillips curve relationship between a measure of unemployment and a subaggregate measure of inflation (services). We generate an aggregate inflation forecast from forecasts of the goods subcomponent separate from the services subcomponent, and compare the aggregated forecast to the leading time-series univariate and standard Phillips curve forecasting models. Our results indicate marked improvements in point and density forecasting accuracy statistics for models that exploit relationships between services inflation and the unemployment rate.

Forecasting future inflation and nowcasting contemporaneous inflation are difficult. We propose a new and parsimonious model for nowcasting headline and core inflation in the U.S. consumer price index (CPI) and price index for personal consumption expenditures (PCE) that relies on relatively few variables. The model's nowcasting accuracy improves as information accumulates over a month or quarter, outperforming statistical benchmarks. In real-time comparisons, the model's headline inflation nowcasts substantially outperform those from the Blue Chip consensus and the Survey of Professional Forecasters. Across all four inflation measures, the model's nowcasting accuracy is comparable to the Federal Reserve Board's Greenbook.

We estimate an empirical model of inflation that exploits a Phillips curve relationship between a measure of unemployment and a subaggregate measure of inflation (services). We generate an aggregate inflation forecast from forecasts of the goods subcomponent separate from the services subcomponent, and compare the aggregated forecast to the leading time-series univariate and standard Phillips curve forecasting models. Our results indicate notable improvements in forecasting accuracy statistics for models that exploit relationships between services inflation and the unemployment rate. In addition, models of services inflation using the short-term unemployment rate (less than 27 weeks) as the real economic indicator display additional modest forecast accuracy improvements.

We examine how a combination of credit market and asset quality information can jointly be used in assessing bank franchise value. We find that expectations of future credit demand and future asset quality explain contemporaneous bank franchise value, indicative of the feedback in credit market information and its consequent impact on bank franchise value.

This paper makes a fundamental contribution by studying loan-loss provisioning over the credit cycle as three distinct phases. Looking at the three distinct phases of the financial crisis—the precrisis period, crisis period, and postcrisis period—is important as loan-loss provisioning is driven by different factors in each, in part due to extensive shifts in (or in the application of) regulatory rule. We show evidence of forward-looking loan-loss provisioning by utilizing Senior Loan Officer Opinion Surveys (SLOOS), which provide useful controls for credit cycle information. Though the SLOOS data set is a restricted sample and generalizability to a broader sample could potentially be a stretch, we control for credit cycle factors as part of an identification strategy to sort out changes in the credit market equilibrium. We contribute to the growing literature on forward-looking loan-loss provisioning and early-in-the-cycle loss recognition by incorporating a broader range of available credit information.

Forecasting future inflation and nowcasting contemporaneous inflation are difficult. We propose a new and parsimonious model for nowcasting headline and core inflation in the U.S. price index for personal consumption expenditures (PCE) and the consumer price index (CPI). The model relies on relatively few variables and is tested using real-time data. The model’s nowcasting accuracy improves as information accumulates over the course of a month or quarter, and it easily outperforms a variety of statistical benchmarks. In head-to-head comparisons, the model’s nowcasts of CPI inflation outperform those from the Blue Chip consensus, with especially significant outperformance as the quarter goes on. The model’s nowcasts for CPI and PCE inflation also significantly outperform those from the Survey of Professional Forecasters, with similar nowcasting accuracy for core inflation measures. Across all four inflation measures, the model’s nowcasting accuracy is generally comparable to that of the Federal Reserve’s Greenbook.

This paper makes a fundamental contribution by studying loan-loss provisioning over the credit cycle as three distinct phases. Looking at the three distinct phases of the financial crisis—the precrisis period, crisis period, and postcrisis period—is important as loan-loss provisioning is driven by different factors in each, in part due to extensive shifts in (or in the application of) regulatory rule. We show evidence of forward-looking loan-loss provisioning by utilizing Senior Loan Officer Opinion Surveys (SLOOS), which provide useful controls for credit cycle information. Though the SLOOS data set is a restricted sample and generalizability to a broader sample could potentially be a stretch, we control for credit cycle factors as part of an identification strategy to sort out changes in the credit market equilibrium. We contribute to the growing literature on forward-looking loan-loss provisioning and early-in-the-cycle loss recognition by incorporating a broader range of available credit information.

In this paper we investigate the forecasting performance of the median CPI in a variety of Bayesian VARs (BVARs) that are often used for monetary policy. Until now, the use of trimmed-mean price statistics in forecasting inflation has often been relegated to simple univariate or "Philips-curve" approaches, thus limiting their usefulness in applications that require consistent forecasts of multiple macro variables. We find that inclusion of an extreme trimmed-mean measure—the median CPI—significantly improves the forecasts of both headline and core CPI across our wide-ranging set of BVARs. While the inflation forecasting improvements are perhaps not surprising given the current literature on core inflation statistics, we also find that inclusion of the median CPI improves the forecasting accuracy of the central bank's primary instrument for monetary policy—the federal funds rate. We conclude with a few illustrative exercises that highlight the usefulness of using the median CPI.

This paper presents a 16-variable Bayesian VAR forecasting model of the U.S. economy for use in a monetary policy setting. The variables that comprise the model are selected not only for their effectiveness in forecasting the primary variables of interest, but also for their relevance to the monetary policy process. In particular, the variables largely coincide with those of an augmented New-Keynesian DSGE model. We provide out-of sample forecast evaluations and illustrate the computation and use of predictive densities and fan charts. Although the reduced form model is the focus of the paper, we also provide an example of structural analysis to illustrate the macroeconomic response of a monetary policy shock.

Our inflation nowcasting model produced relatively accurate nowcasts over a long historical sample period and over the shorter period 2020–2022.

Median and trimmed-mean inflation rates tend to be useful estimates of trend inflation over long periods, but they can exhibit persistent departures from the underlying trend over shorter horizons. In this Commentary, we document that the extent of this bias is related to the degree of skewness in the distribution of price changes. The shift in the skewness of the cross-sectional price-change distribution during the pandemic means that median PCE and trimmed-mean PCE inflation rates have recently been understating the trend in PCE inflation by about 15 and 35 basis points, respectively.

We examine the predictive relationship between various measures of inflation expectations and future inflation. We find that the expectations of professional economists and of businesses have tended to provide more accurate predictions of future inflation than the expectations of households and of financial market participants. However, the forecasts coming from a relatively simple and popular benchmark inflation forecasting model have historically been roughly as accurate as the expectations of businesses and professional economists.

This Commentary builds on recent research separating the components of overall inflation into cyclical and acyclical categories, but it does so at a finer level of disaggregation than previous analyses to understand recent inflation developments in the two categories. The inflation rate among cyclically sensitive subcomponents, which comprise roughly 40 percent of overall core PCE inflation, has generally continued to firm in recent years in line with a strengthening labor market and has returned to near pre-Great Recession levels. By contrast, the inflation rate among the acyclical subcomponents remains subdued. A modest firming in acyclical core PCE inflation to a more normal level, combined with ongoing strength in the labor market, would be enough to return core PCE inflation to 2 percent within approximately one year.

Using a flexible statistical model to project inflation outcomes into the future, this Commentary finds that the most likely path for inflation based on recent inflation dynamics is generally similar to what would have been expected given inflation dynamics in the late 1990s, but there is more uncertainty around the forecast now than in the late 1990s.

This Commentary examines inflation forecasts generated from a range of statistical models that historically have performed well at forecasting inflation. For each model, we look at the most likely future forecast path and the distribution of forecasts around that path. We show that the models project generally rising inflation, but, in contrast to other forecasts, five out of six models assign a less than 50 percent probability to inflation’s being 2 percent or higher over the next three years.

Monetary policymakers often use simple monetary policy rules, like the Taylor rule, as an input into their decision-making. However, there are many different simple rules, and there is no agreement on a single “best” rule. We look at the federal funds rates coming from seven simple rules and three economic forecasts to investigate the range of results that can be produced. While there are some commonalities, we document that the differences in the federal funds rates suggested by the rules can be quite pronounced.

Looking across a range of statistical models, we consider the likely path of future inflation and the uncertainty surrounding the models’ predictions. The models suggest that inflation is on a rising path, and while inflation forecast uncertainty is somewhat elevated relative to the norms of the last 20 years, core inflation uncertainty is relatively low. For both inflation rates, forecast uncertainty is much lower as of the first quarter of 2015 than it was around the Great Recession.

We take a closer look at the connections between wages, prices, and economic activity. We find that causal relationships between wages and prices are difficult to identify, and the ability of wages to help predict future inflation is limited. Wages appear to be useful in assessing the current state of labor markets, but they are not necessarily sufficient for thinking about where the economy and inflation are going.

Using a statistical model, we find that three factors explain most of the decline in residential investment at the end of 2013 and the beginning of 2014: the increase in mortgage rates since early 2013, the unusually cold winter, and a modest tightening of lending standards in the residential mortgage market. Future prospects for residential investment depend heavily on mortgage rates. A return to normal weather and easing lending standards would boost activity, but even moderate increases in mortgage rates through the end of next year could restrain residential investment going forward.

A standard Taylor rule, which expresses the federal funds rate as a function of inflation, the unemployment gap, and the past federal funds rate, tracks the federal funds rate well over time. We improve the fit by adding employment growth. Then we evaluate the effectiveness of that rule in a new way—by how accurately it predicts whether the FOMC moves the fed funds rate at its next meeting. It does pretty well, predicting nearly 70 percent of the time correctly.

The Federal Open Market Committee has been providing guidance to help markets anticipate when it will begin raising the federal funds rate target. The most recent guidance suggests that the target will not change at least until after an unemployment or inflation threshold is breached. We use a forecasting model to estimate when these thresholds are likely to be breached. We also consider how an inflation floor would affect the timing of liftoff.

A simple but powerful technique for incorporating a changing underlying inflation trend into standard statistical time series models can improve forecast accuracy significantly-about 20 percent to 30 percent, two to three years out.

Should the unanticipated slowing of inflation that has occurred since early 2012 raise doubts about the reliability of inflation forecasts? Our analysis indicates that inflation fell well within a normal range of uncertainty, and most of the deviation from the original forecast was a response to other economic developments.

The Median CPI is well-known as an accurate predictor of future inflation. But it’s just one of many possible trimmed-mean inflation measures. Recent research compares these types of measures to see which tracks future inflation best. Not only does the Median CPI outperform other trims in predicting CPI inflation, it also does a better job of predicting PCE inflation, the FOMC’s preferred measure, than the core PCE.

In the wake of Great Recession, the Federal Reserve engaged in conventional monetary policy actions by reducing the federal funds rate. But soon the rate hit zero, and could go no lower. In such environments, policymakers still think in terms of where the federal funds rate should be, were it possible to go negative. To project the “unconstrained path” of the funds rate—ignoring the zero lower bound—and to identify the key underlying shocks driving that path, we employ a statistical macroeconomic forecasting model. We find that the federal funds rate would have been extremely negative during 2009-2010.

Models of the macroeconomy have gotten quite sophisticated, thanks to decades of development and advances in computing power. Such models have also become indispensable tools for monetary policymakers, useful both for forecasting and comparing different policy options. Their failure to predict the recent financial crisis does not negate their use, it only points to some areas that can be improved.

Sharp rises in energy and other commodity prices have recently ignited concerns about inflation. Will these price increases spill over to other prices more generally? We study the typical responses of different price shocks and assess whether the recent behavior of producer and consumer prices is consistent with historical norms. Our analysis shows that the behavior of various producer and consumer prices since late 2009 has generally matched up with historical patterns. Overall, our findings suggest that effects of the recent energy and commodity price shocks on core consumer prices will be modest going forward.

Knowing whether buying a home is a better financial move for a family than renting requires a consideration of costs and options that people often neglect to factor in. One aspect of the calculation that is almost always overlooked is uncertainty—the fact that no matter how good one’s estimates of the future are, the future can turn out differently than projected. Incorporating uncertainty into the rent-or-buy calculation gives potential homebuyers information that can improve their decisions. While incorporating uncertainty is complicated, it’s made easier with the Cleveland Fed’s online calculator.

The past recession has hit the labor market especially hard, and economists are wondering whether some fundamentals of the market have changed because of that blow. Many are suggesting that the natural rate of long-term unemployment— the level of unemployment an economy can’t go below—-has shifted permanently higher. We use a new measure that is based on the rates at which workers are finding and losing jobs and which provides a more accurate assessment of the natural rate. We fi nd that the natural rate of unemployment has indeed shifted higher—but much less so than has been suggested. Surprising trends in both the job-finding and job-separation rates explain much about the current state of the unemployment rate.

Since the 1970s, productivity growth in the manufacturing sector has outpaced the overall economy, yet the sector’s share of the workforce has declined dramatically. This leads us to ask if we are in fact engineering ourselves out of jobs. This Economic Commentary explores the relationship between productivity and employment and points out why this apparently straightforward relationship may be more complicated than it appears.