In search of a robust inflation forecast.

Brave, Scott ; Fisher, Jonas D.M.

Introduction and summary

The sound conduct of monetary policy is the bedrock on which a well-functioning economy rests. In the United States, the conduct of monetary policy is guided by the goals set out in the 1977 amendment to the Federal Reserve Act of 1913. According to this amendment, the Federal Reserve System and the Federal Open Market Committee (FOMC) should conduct monetary policy to promote the goals of "maximum" employment and output and to promote "stable" prices.

Of these goals, the primary focus, many economists believe, should be on achieving price stability. A stable price level means that prices of goods and services are undistorted by inflationary surprises. This enhances the role of prices in providing signals to ensure the efficient allocation of resources and the maximum possible sustainable level of employment. Many also believe that a stable price level encourages saving and capital accumulation, because it prevents asset values from being eroded by unanticipated inflation or debt being amplified by unanticipated deflation. This should also contribute to the goals of attaining maximum employment and output.

For these reasons, monetary policy is heavily influenced by factors thought to affect the rate of change of prices, that is, inflation. Until recently, the dominant concern had been a recurrence of past episodes of high inflation that have been associated with bad macroeconomic outcomes. In recent years, however, concern has shifted to the possibility of deflation. In either case, given the long lags over which policy actions can take effect, it is often necessary for the FOMC to take action before inflation starts to move in an undesired direction. The only way to do this with some confidence is to have effective ways of predicting the future course of inflation. Hence, forecasting inflation is a crucial ingredient in the formulation of monetary policy.

This article is concerned with the ability to forecast inflation. This is a relevant issue since recent work has cast doubt on the reliability of traditional approaches to forecasting inflation. Inflation forecasting is usually conducted with statistical models based on some version of the Phillips curve, the statistical relationship between inflation and overall aggregate economic activity. The recent literature suggests that this approach has not been reliable. In particular, Atkeson and Ohanian (2001) found that over the period 1985-99, one-year-ahead forecasts of inflation based on the Phillips curve do no better than a "naive" forecast where the forecast is set to the inflation rate over the prior year.

Some researchers have come to the defense of traditional forecasting models, arguing that the failure pointed out by Atkeson and Ohanian (2001) is special to the sample period they consider. (1) Still, it is difficult to dismiss their finding out of hand. As is clear from the work of Stock and Watson (1999, 2002, 2003), the forecasting failure in the post-1985 period reflects a more fundamental problem. While particular inflation forecasting models may do well in some periods, more often than not these models perform poorly at other times. It is not enough for a forecasting model to do well in just the recent period, because it is also important to guard against the possibility of structural change. Forecasters need to know that their forecasting strategy is robust to changes in the economic environment that are not noticed until well after they have occurred.

This article, therefore, addresses the question: Is it possible to build a robust inflation forecasting framework that does well in the recent period as well as earlier periods? We find that the answer to our question is "yes," although the gains compared with models based only on past inflation are at times quite modest. However, around periods in which inflation begins to pick up, the best models we consider show clear advantages over inflation-only models.

We address our question by considering the out-of-sample forecasting performance of a large set of models. We study forecast errors for the one-year and two-year forecasting horizons and at the monthly and quarterly frequencies. Our notion of robustness is that the model consistently lies near the top of performance lists of alternative models and is consistently more successful than models based only on past inflation, such as Atkeson and Ohanian's naive model.

Our main findings are as follows. First, consistent with previous studies, we show that different inflation indicators do well at forecasting inflation at different times. This makes the basic point that one should not rely on the "indicator du jour" when assessing the inflation outlook and that forecasters should be looking at many different indicators.

Second, we show that individual forecasting models that combine data in different ways do not consistently outperform the naive model (which turns out to be superior to other inflation-only models) in terms of mean-squared errors. For example, in some periods the naive model is better; at other times there is at least one model that does better than the naive model, but it is never the same one. This is true at both the one-year and the two-year horizon and with monthly and quarterly data. These findings are consistent with those reported by Fisher, Liu, and Zhou (2002).

Third, we show that certain kinds of models based on weighted averages of forecasts from individual models consistently outperform the naive model and other models based only on past inflation. This is true for both monthly and quarterly data and at both forecast horizons. At the one-year horizon, the best model involves weights computed using the within-sample forecasting performance of the individual models. At the two-year horizon, the best model uses a simple average of the individual models. For both forecasting horizons, the best versions of these models use a rolling window of data for the forecast, and these models are typically superior to the individual models for all sub-samples considered. These findings lead us to conclude that the most robust forecasts combine information from several different forecasting models, each of which incorporates the information in the available inflation indicators in different ways.

Another finding is that data available at the quarterly frequency that are not available at the monthly frequency appear to add little additional information to our forecasts. This might seem surprising, given that existing theoretical models suggest that data on real unit labor costs and productivity should be useful for predicting inflation, and these data are only available at the quarterly frequency. Still, we find that the additional data do not improve our forecasts very much, suggesting that most of the information about future inflation in the quarterly data is already incorporated in the monthly series we consider.

Below, we describe the different models we consider. Then, we discuss the methodology for assessing the forecasting performance of these models and present our findings.

Statistical models of inflation

In order to leave no stone unturned in our quest for a robust framework for forecasting inflation, we consider a large number of models. These models involve different ways of incorporating the vast amount of data available to the inflation forecaster. In principle, almost all the available macroeconomic data contain some information about future inflation. The challenge is to find a way to incorporate this information into a forecasting model. There are many ways to do this. One way would be to summarize the information useful for forecasting inflation before it is put into a model. Another approach would be to summarize the relevant information after it has been included in individual models. We employ each of these methods and also combine aspects of both. Finally, we combine the forecasts from several different types of models, each of which involves a different approach to forecasting. In the sub-sections that follow, we describe examples of each of these approaches. Many of these examples are motivated by the work of Stock and Watson (1999, 2002, 2003). For convenience we focus on the monthly frequency case. It should be clear how to extend the models to the quarterly frequency case. Table 1 summarizes the models underlying our analysis.

The basic regression equation

All the models we consider have as their foundation the basic regression equation:

1) [[pi].sup.12.sub.t+J] - [[pi].sup.12.sub.t] = [alpha] [beta](L)([[pi].sub.1] - [[pi].sub.t-1]) + [[K.summation over (i=1)] [[theta].sub.1] (L)[x.sub.it] + [[epsilon].sub.t+J], J = 12, 24.

This equation relates changes in the 12-month inflation rate, defined as the 12-month change in the natural logarithm of the price index [p.sub.t],

[[pi].sup.12.sub.t] = ln [p.sub.t] - ln [p.sub.t-12],

to past values of the one-month inflation rate, [[pi].sub.t],

[[pi].sub.t] = ln [p.sub.t] - ln [p.sub.pt-1],

and past values of other variables deemed useful for forecasting inflation, [x.sub.it], i = 1, 2, ..., K. In equation 1, [alpha] is a constant and [beta](L) and [[theta].sub.i](L), i = 1, 2, ..., K, specify the number of lags in inflation and other variables included in the equation. The number of other variables included is given by K, which is greater than or equal to zero. (2) We estimate equation 1 by ordinary least squares and use a standard lag selection criteria to choose the number of lags of inflation and other variables. (3) We allow for the possibility that lags could vary from one month to a year.

For given estimates of the coefficients in equation 1 at date T, [[??].sub.T], [[??].sub.T], (L), and ([[??].sub.iT] (L), the date T forecast of 12-month inflation J periods ahead using the basic regression equation is (4)

2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Models based only on inflation

We consider two models based only on inflation. The first is the "naive" model described by Atkeson and Ohanian (2001). The naive model can be viewed as a special case of equation 1, where [[alpha].sub.T] = [[beta].sub.T](L) = K = 0. That is, the naive model equates the date T forecast of inflation over the next 12 months, [[??].sup.12.sub.T+12], with its value over the most recent 12-month period,

3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Similar to the 12-month forecast, the naive model equates the date T forecast of 12-month inflation 24 months into the future, [[??].sup.12.sub.t+24], with its most recent value:

4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The other model based only on inflation is called the autoregression model. This model postulates that changes in 12-month inflation only depend on recent changes in one-month inflation, that is, it sets K = 0 in equation 1.

Single equation models with inflation indicators

We consider three models that involve implementing equation 1 with K = 1. For the natural rate model, [x.sub.1t] is set equal to the difference between a measure of the actual unemployment rate and an estimate of the "natural rate." (5) The output-gap model, is similar. In particular, [x.sub.1t] is set equal to the difference between a measure of aggregate output and an estimate of "potential" output, where the latter is estimated using the same approach as with the natural rate.

For the activity model, [x.sub.1t] is the Chicago Fed National Activity Index (CFNAI). This index is a weighted average of 85 monthly indicators of real economic activity. The CFNAI provides a single, summary measure of a common factor in these national economic data. As such, historical movements in the CFNAI closely track periods of economic expansion and contraction. (6)

Multiple equation models with inflation indicators

We also consider models that combine forecasts from applying versions of equation 1 with different indicator variables. The diffusion model can be viewed as a generalization of the activity model. We use a small number of indexes that explain the movements in 145 macroeconomic time series, including data measuring production, labor market status, the strength of the household sector, inventories, sales, orders, financial markets, money supply, and price data. The procedure that obtains the indexes processes the information in the 145 series, so that each index is a weighted average of the series and each index is statistically independent of the others. We consider six indexes computed in this way, [d.sub.1t], [d.sub.2t], ..., [d.sub.6t]. These are listed in descending order in terms of the amount of information embedded in them. (7) The diffusion model involves first calculating an inflation forecast based upon including [x.sub.1t] equal to the index with the most information, [d.sub.1t]. We repeat this exercise five times, successively including one more index in descending order of importance. For instance, the third forecast created includes the three most important indexes, [d.sub.1t], [d.sub.2t], and [d.sub.3t], as [x.sub.1t], [x.sub.2t], and [x.sub.3t]. The forecast from the diffusion model is the median of these six forecasts. (8)

Consider a list of forecasts of 12-month inflation J periods ahead at date T. Index these forecasts by n and denote them [f.sub.T+J](n). The combination model is the median of these forecasts,

5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where the set of forecasts, S, is derived from the same 145 variables used to compute the diffusion indexes. In particular, each forecast [f.sub.T+J](n) is based on equation 1 with K = 1 and [x.sub.1t] set equal to one of the 145 variables used in the diffusion model.

The indicator model is based on a smaller list of variables grouped into six categories: economic activity, slackness measures, housing and building activity, industrial prices, financial markets, and, for the quarterly case only, productivity and marginal cost. Within each group, we compute a forecast using equation 1 with K = 3, [x.sub.1t] set equal to the change in the federal funds interest rate, [x.sub.2t] set equal to the unemployment rate, and [x.sub.3t] to one of the variables in the group of indicators. We average the forecasts within each group. Then the indicator model forecast is based on equation 5 with [f.sub.T+J] (n) corresponding to one of the average forecasts from the five categories and S corresponding to the set of five average forecasts.

The combination and indicator models are useful to consider since they represent two alternatives to index-based methods for summarizing the information in many variables. The combination model is directly comparable to the diffusion model in that it involves the same set of variables. Therefore, it is useful to assess which method is superior for incorporating the information in a large number of variables. We work with the indicator model for two reasons. First, experience has shown it to be a relatively reliable approach to forecasting. Second, since it involves a small list of indicators, it represents a compromise between models that put a lot of weight on a single indicator, such as the natural rate and output gap models, and models that take virtually no stand on which indicators are useful, such as the diffusion and combination models.

Meta models

The preceding discussion introduced six models in addition to the inflation-only naive and autoregression models. To summarize, these models are the natural rate, output gap, activity, diffusion, combination, and indicator models. As we show below, none of these models consistently outperforms the inflation-only models over the various sub-samples we consider. However, for most of the sub-samples, at least one of the models does outperform the inflation-only models. This raises the question of whether it is possible to combine the information in these individual models to arrive at a superior forecast. The final group of models we study are designed to do just this. We call them meta models. (9)

Consider a list of forecasts of 12-month inflation J periods ahead at date T generated by the models listed above. Index these forecasts by n and denote them [f.sub.T+J] (n). The forecast of a given meta model is

6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where M is the set of models from which the meta model is constructed and [w.sub.n,T] is the weight attached to model n at date T. Equation 6 says that the forecast is set equal to a weighted average of the forecasts of the models comprising the meta model.

The meta models we consider differ according to the set of models from which the forecast is constructed and the manner in which the weights are computed. In the equally weighted models, the weights are all set equal to the inverse of the number of models comprising the model. That is, these forecasts are just the average over the forecasts of the individual models. The optimally weighted meta models have weights computed for each forecast date. These weights are computed as follows. At each forecast date, there is a prior history of forecasts and a history of actual inflation realizations corresponding to these forecasts. We reset the weights in equation 6 each forecast date to equal the coefficients of a regression of realized inflation on the forecasts using data on these variables available up to the date of the forecast.

Model evaluation methodology

We evaluate the accuracy of the models by comparing them with the naive and autoregression models. A modeling strategy will be deemed to be "robust" if it lies near the top of performance rankings and outperforms models based only on past inflation consistently across the various sub-samples we consider. We assess performance by simulated out-of-sample forecasting. This involves constructing inflation forecasts that a model would have produced had it been used historically to generate forecasts of inflation. We study forecasts of personal consumption deflator inflation, excluding food and energy, that is, core personal consumption deflator inflation. (10)

Two drawbacks of this approach are 1) we assume all the data are available up to the forecasting date, and 2) we do not use real-time data in our forecasts. (11) On a given date particular data series may not yet be published. Also many data series are revised after the initial release date. In our forecasting exercises, we compute forecasts and calculate the CFNAI and diffusion indexes assuming all the series underlying the forecasts and the indexes are available up to the forecast date. In practice this is never the case. Since we do not use real-time data, we also abstract from problems associated with data revisions. We suspect 1) and 2) lead us to overstate the effectiveness of our models. (12)

Root mean-squared error criterion

Our performance measure is the standard root mean-squared error (RMSE) criterion. The RMSE for any forecast is the square root of the mean squared differences between the actual inflation rate and the predicted inflation rate over the period for which simulated forecasts are constructed. For J = 12, 24

7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where T - J denotes the number of forecasts made over the period under consideration. (13)

An advantage of the RMSE measure of performance is that its units are the same as inflation. This means, for example, the magnitude of RMSE for a given model can be directly compared with the average rate of inflation over the sample period. Another advantage is that large forecast errors are given more weight than small errors. Presumably, we care more about large mistakes than small mistakes. At the same time, a potential drawback of the RMSE measure is that it weights positive and negative errors of the same size in the same way. If we are more concerned about inflation increases than decreases, then this is definitely a drawback. Recent debates about the possible perils of deflation suggest that inflation decreases, at least at low levels of inflation, are certainly a concern of policymakers and so they should not be ignored. It would be interesting to consider other measures of forecast performance that weight increases and decreases in inflation differently, depending on the prevailing level of inflation.

Data and sample periods

The data we use in the analysis are described in the data appendix. The sample period of our analysis begins in 1967. We choose this date because it is the beginning date for the data used to construct the CFNAI and the diffusion indexes. We estimate the forecasting equations using all the data available at the time of the forecast and also consider the method of rolling regressions. A rolling regression keeps the number of observations in the regression constant across forecasts. Since it excludes observations from the distant past, this approach can in principle accommodate the possibility that there has been structural change in the data-generating process. To implement the rolling regression procedure, we choose a sample length of 15 years.

Finally, we consider four distinct periods over which to evaluate the forecasts of the models: 1977-84, 1985-92, 1993-2000, and 2001-2003. The first three periods are all 96 months long. We also consider the 1985-2003 period. The 1977-84 period is a period of high inflation volatility and general economic turbulence. The 1985-92 period is generally associated with a new monetary policy regime. This period also includes a mild recession. The 1993-2000 period witnessed uninterrupted economic expansion, stable monetary policy, and declining inflation. The 2001-2003 period is interesting because it involves recent forecast performance.

Findings

Next, we describe our findings. We focus on the monthly results and only discuss the findings with quarterly data at the end.

The best indicator keeps changing

Before evaluating our models, it is useful to consider the forecast performance of individual indicators. Each forecast is based on equation 1 with K = 1 and [x.sub.1t] set equal to one of the list of indicators that includes the union of the set of variables used in the indicators model and the combination (or diffusion) model. Table 2 shows the top five indicators for the sample periods 1977-84, 1985-92, 1993-2000, and 2001-03. The key thing to notice from this table is that the list keeps changing! In the earliest sub-sample, indicators of manufacturing activity seem to do best at both the one-year and two-year horizons. At other times, employment, housing, or financial indicators do well. Overall, variables that do well at the one-year horizon do not necessarily do well at the two-year horizon. The lesson to be learned here is: beware of the indicator du jour. (14)

The best model keeps changing, too

Table 3 (p. 19) shows the performance of all the models (except for the output-gap model, which we only consider at the quarterly frequency) for the one-year and two-year forecast horizons, respectively. The meta models are in bold type. We discuss these models in the following sub-section. In table 3, we list the models for the four sub-samples as well as the period 1985-2003. We also display some useful summary statistics. For each sample period, we show the RMSE of the best model, the range of RMSE across forecasting models, the absolute value of the difference between the naive model and the best model, and average actual inflation.

The first thing to notice is that for both forecast horizons and across all sample periods the naive model performs better than the autoregression model. That is, there is no more information about future inflation in past inflation than that already contained in the most recent reading of 12-month inflation. This fact motivates our focus on using the naive model as a benchmark for comparison.

Now, consider the one-year ahead forecasts. In the earliest period, 1977-84, the natural rate model performed best. The magnitudes of the errors from this forecast are about one-sixth of the average inflation rate in this period. This is large relative to the amount by which this best model outperforms the naive model; the difference between the best model and the naive model is only about one-thirtieth of the average inflation rate in this period. So, even in this early period, the naive model is difficult to beat.

Since 1985, it has been even harder to beat the naive model. Indeed, over the entire 1985-2003 period the naive model is the best performer of the individual models. Consistent with the findings in Fisher, Liu, and Zhou (2002), the success of the naive model is concentrated in the 1985-92 period. In the latter part of the post-1985 sample, there is a model that beats the naive model, but this model changes and the extent of the victory is quite small. We should not attribute too much to the differences among the models for this forecast horizon; the range of root mean-squared errors is never that large and in the recent period is only about two-tenths of a percentage point.

The two-year ahead forecasts in table 3 present a similar picture. No individual model does well across all the sub-samples, although the diffusion model does perform reasonably well. The naive model does surprisingly well after 1985. Indeed, over the entire 1985-2003 period it is only one-tenth of a percentage point worse than the best individual model for this period, the diffusion model. The range of forecast errors is, as expected, a little larger for the two-year ahead forecasts, but still quite small.

Overall, table 3 indicates that no individual model consistently beats the naive model, and when one model does do better, the gains are small. We conclude that the natural rate, activity, diffusion, combination, and indicator models are not robust inflation forecasting frameworks.

Finally, it is interesting to note the relative performance of the combination, diffusion, and indicator models. Recall that these models involve using many indicators to forecast inflation, but do so in different ways. At the one-year horizon, there is little to choose between the models. Indeed the difference between the models is always less than one-tenth of a percentage point (not shown). At the two-year horizon, the diffusion model consistently outperforms the other two models except for the most recent period. Here the gains are more substantial (also not shown). For example, the diffusion model is superior to the indicator model by over 1 percentage point in the pre-1985 period and superior to the combination model by eight-tenths of a percentage point. In the post-1985 period the gains are about two-tenths and one-tenth of a percentage point, respectively.

The gains to combining forecasts

We now consider what happens when we combine the information in the forecasts from the various models. That is, we add to the list of models compared with the naive model the equally weighted and optimally weighted meta models. For good measure, we throw meta models based on rolling regressions into the mix. These are indicated in the table by the term "rolling." The meta models are indicated by bold type in table 3. Since the optimally weighted models require a sample of forecasts to compute the weights, we only include these models in the mix after 1985. The meta models consist of the naive, natural rate, indicator, activity, diffusion, and combination models.

Notice that for both forecast horizons, the meta models generally outperform the individual models. Moreover, there is always a meta model that outperforms the naive model no matter which sub-sample we consider. Of special note is that it is possible to beat the naive model in the challenging 1985-92 period. Still, overall, the gains over the naive model are modest. Using the rolling regression approach provides some additional gain. At the one-year horizon, the regression strategy for computing weights seems to do better than just averaging the forecasts, but at the two-year horizon the opposite is true.

Is there evidence of a robust model here? Looking at the different sample periods and forecast horizons, it seems that the rolling optimally weighted model consistently outperforms the naive model and is near the top of the performance lists for the one-year horizons. The rolling equally weighted model is a very good performer at the two-year horizon. In both cases, when the model is not at the top of the performance list, it is within one-tenth of a percentage point of the top model and usually much less than that. The gains relative to the naive model are small in the 1985-92 period, but there are gains. Since 1993, the best meta-models beat the naive model by about one-tenth of a percentage point at the one-year horizon and two-and-a-half-tenths at the two-year horizon. This latter advantage is not insubstantial given that inflation over this period is on average less than 2 percent.

The robust models

Since 1985, the most robust models seem to be the rolling equally weighted and rolling optimally weighted models. It is instructive to study these models a little more.

Cumulative forecast errors

Figures 1 and 2 display cumulative squared forecast errors for the rolling optimally weighted model and the naive model for the one-year and two-year horizons. Figures 3 and 4 (p. 22) are similar, but with the rolling equally weighted and naive models. The vertical lines in these figures indicate the boundaries of the sample periods we consider. To interpret these figures, note that differences in performance are indicated by differences in the slopes of the lines. The model with the flatter line is performing better than the other model over the particular period in which the line is flatter. When one line is below another at a particular date, the model associated with that line has performed better in an RMSE sense up to that date. Note that, due to the need to have data to compute the weights, the figures for the rolling optimally weighted model begin in 1985.

[FIGURES 1-4 OMITTED]

Consider the rolling optimally weighted model first. For the one-year horizon there is little to choose between this model and the naive model in the 1985-92 period. Differences emerge after 1993, but these are concentrated in 1994 and 1995. Additional gains relative to the naive model appear in 2003, though. For the two-year horizon the differences are more substantial, but the overall impression is similar. The location of when the largest gains appear is interesting, since these correspond to periods in which inflation was increasing.

The figures for the rolling equally weighted model present a similar picture for the post-1985 period. The pre-1985 observations are particularly interesting. These illustrate the fact that most of the gains relative to the naive model are in the period before 1985. We can see this in the distance between the two lines in the figures, which does not get much wider after 1985.

Model weights

Figures 5 and 6 (pp. 23-24) display the evolution of the weights underlying the rolling optimally weighted model for the one-year and two-year horizons, respectively. Recall that these weights are based on regressing actual inflation on forecasts from six models, the naive, activity, natural rate, indicator, combination, and diffusion models. The individual models are estimated using rolling regressions, but the weights are based on forecasts for the entire available sample.

[FIGURES 5-6 OMITTED]

Figure 5 shows that for much of the sample all the models get a non-trivial weight for the one-year horizon. Except for the early part of the sample, the weights have not changed that much. Still, their time paths provide some interesting insight into the evolution of the economy. For example, the natural rate model has declined in importance over the sample. Nonetheless, it still gets a large weight. The weight on the naive model has grown over the sample. The activity, diffusion, and combination models get negative weights. (15) Figure 6 indicates that forecasting the two-year horizon involves using the models differently. The natural rate model gets much less weight, and for much of the sample the activity and indicator models get very small weights. Consistent with their individual performances (see table 3), the naive and diffusion models get large weights.

Quarterly data

Now, we briefly summarize our findings with quarterly data. To conserve space we do not display our findings. Our purpose here is twofold. We want to know whether averaging the forecasts obtained by different forecasting procedures also improves forecasts at the quarterly frequency. We also want to understand whether adding quarterly data to the analysis that are not available at the monthly frequency improves the quality of the forecasts. The new data include data from the National Income and Product Accounts, the output gap, and data on productivity and costs (see the appendix for a list of the specific series).

Regarding the first question, we find that the basic principle of averaging different forecasts also yields forecasting benefits at the quarterly frequency. Indeed the same meta models that show promise at the monthly frequency are also among the most robust at the quarterly frequency when we include the additional quarterly data. (16) With one exception, these models improve on the naive forecast over all sub-samples and both forecast horizons we consider. The exception is in the 1985-92 period for the one-year horizon, in which no model is superior to the naive model.

Incorporating the additional data leads to mixed results. We use the third month in each quarter to compare a given monthly model with its quarterly counterpart. When we do this and compare corresponding monthly and quarterly models, we find little evidence that the additional data improve the forecasts. In particular, there is not a consistent pattern of improvement with the quarterly models and when there is improvement it is typically much less than one-tenth of a percentage point. Sometimes the quarterly models are worse. One model does show consistent improvement at the quarterly frequency--the rolling optimally weighted model. This model does well at the two-year horizon, improving over its monthly counterpart by about one-tenth of a percentage point in all sub-samples after 1985. (17)

In a departure from the monthly analysis, a non-meta model shows up in the list of robust models when we incorporate the additional data. This model is the rolling output gap model, which we could not examine at the monthly frequency because gross domestic product data are only available quarterly. When the output gap model is estimated using the rolling procedure, it is the best performing model over 1977-84 and 1985-2003 and performs better than the naive model in all the sub-samples we consider when forecasting two years ahead. This model does not do as well forecasting at the one-year horizon. In particular, it is outperformed by the rolling optimally weighted model over all the sub-samples. Still, the fact that such a simple model does so well at forecasting two years ahead is interesting and deserves further study. (19)

Taking all the evidence into account, it seems reasonable to conclude that the quarterly data do not add much to forecast performance. Two exceptions are when the additional data are incorporated into the rolling output gap model and the rolling optimally weighted model, both of which perform well at the two-year horizon.

Conclusion

We have found that a robust forecast of the magnitude of inflation can be obtained by combining the forecasts of several models that incorporate the information in the available data in different ways. This suggests that a useful approach to building a reliable statistical forecasting framework is to be eclectic with respect to both the data used to formulate a forecast and the models used to incorporate the data into a forecast. Relying on a small number of inflation indicators and one forecasting model is not a good idea.

Having drawn this conclusion, we must note two caveats. (18) The most obvious caveat is that the conclusion we have just stated sows the seeds of future failure. We have concluded that one must not rely on a particular model, yet we have essentially described a particular model. While we realize the circularity of our conclusion, we would rather interpret our findings as suggesting that combining the forecasts from models that include the data in different ways is the main lesson to be learned. That is, we do not put a lot of weight on the particular models we worked with. We also want to emphasize the limitations of the kinds of forecasting models studied in this article. Clearly, these models are not structural and, therefore, are inadequate for assessing the impact of systematic changes in policy. This is what fully articulated general equilibrium economic models, which account for behavioral responses to policy changes, are for. However, such models, while beginning to be used at central banks, are still inadequate for the everyday needs of policymakers. The forecasting models discussed here have their uses and probably will continue to be popular for some time to come. Principally, these models are useful for understanding what current inflation expectations are. Since the past actions of the Fed are embedded in the coefficients, the models take into account "typical" Fed responses to current conditions. For these reasons, inflation forecasts serve as a useful benchmark for policymakers assessing the current stance of monetary policy. This article has shown that such forecasts can be improved reliably by taking into account information in variables other than inflation.

DATA APPENDIX

Monthly data: 1967:01-2003:12 (a)

Model Transformation

Activity log 1st diff
Activity 1st diff
Activity 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log
Activity, diffusion, combination log
Activity, diffusion, combination log
Activity, diffusion, combination log
Activity, diffusion, combination log
Activity, diffusion, combination log
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination level
Activity, diffusion, combination level
Activity, diffusion, combination level
Activity, diffusion, combination level
Activity, diffusion, combination level
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, combination log 1st diff
Activity, diffusion, log
 combination, indicators (3)
Activity, diffusion, 1st diff
 combination, indicators (2)
Activity, diffusion, log 1st diff
 combination, indicators (2)
Activity, diffusion, 1st diff
 combination, indicators
Activity, indicators (2) level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 1st diff
Diffusion, combination log 2nd diff
Diffusion, combination (a) log 1st diff
Diffusion, combination log 1st diff
Diffusion, combination 1st diff
Diffusion, combination 1st diff
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination log 1st diff
Diffusion, combination level
Diffusion, combination log 1st diff
Diffusion, combination log 1st diff
Diffusion, combination 1st diff
Diffusion, combination 1st diff
Diffusion, combination level
Diffusion, combination level
Diffusion, combination 1st diff
Diffusion, combination 1st diff
Diffusion, combination level
Diffusion, combination level
Diffusion, combination level
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination log 2nd diff
Diffusion, combination 1st diff
Diffusion, combination, log 2nd diff
 indicators (5)
Diffusion, combination, 1st diff
 indicators (5)
Diffusion, combination, 1st diff
 indicators
Diffusion, combination, log 2nd diff
 indicators (4)
Diffusion, combination, log 2nd diff
 indicators (4)
Diffusion, combination, level
 indicators (4)
Indicators (1) log 1st diff
Indicators (3) log 1st diff
Indicators (3) log 1st diff
Indicators (1) log 1st diff
Indicators (1) level
Indicators (5) level
Indicatorsb (5) level
Indicators (5) log 1st diff
Indicators (5) log 1st diff
Indicators (4) log 1st diff
Indicatorsc (3) log 1st diff
Indicators (4) log 1st diff
Indicatorsd (4) log 1st diff
Indicators (4) log 1st diff
Indicators (4) log 1st diff
Natural rate band-pass filtered
Prices log 2nd diff

Model Mnemonic

Activity le
Activity lrm25
Activity
Activity, diffusion, combination cbhm
Activity, diffusion, combination cdbhm
Activity, diffusion, combination cnbhm
Activity, diffusion, combination csbhm
Activity, diffusion, combination ypdhm
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination hsm
Activity, diffusion, combination hst
Activity, diffusion, combination hstmw
Activity, diffusion, combination hstne
Activity, diffusion, combination hsts
Activity, diffusion, combination hstw
Activity, diffusion, combination ip
Activity, diffusion, combination ip51
Activity, diffusion, combination ip511
Activity, diffusion, combination ip512
Activity, diffusion, combination ip521
Activity, diffusion, combination ip53
Activity, diffusion, combination ip531
Activity, diffusion, combination ip532
Activity, diffusion, combination ip54
Activity, diffusion, combination ipb0
Activity, diffusion, combination ipfp
Activity, diffusion, combination ipmdg
Activity, diffusion, combination ipmfg
Activity, diffusion, combination ipmnd
Activity, diffusion, combination iptp
Activity, diffusion, combination iputl
Activity, diffusion, combination laconsa
Activity, diffusion, combination ladurga
Activity, diffusion, combination lafirea
Activity, diffusion, combination lagooda
Activity, diffusion, combination lagovta
Activity, diffusion, combination lamanua
Activity, diffusion, combination laminga
Activity, diffusion, combination lanagra
Activity, diffusion, combination landura
Activity, diffusion, combination lapriva
Activity, diffusion, combination lartrda
Activity, diffusion, combination laserpa
Activity, diffusion, combination LASRVSA = lainfoa
 + lapbsva + laeduha
 + laleiha + lasrvoa
Activity, diffusion, combination LATPUTA = lattula
 - lawtrda - lartrda
Activity, diffusion, combination lena
Activity, diffusion, combination lhelpr
Activity, diffusion, combination lomanua
Activity, diffusion, combination lrmanua
Activity, diffusion, combination napmc
Activity, diffusion, combination napmei
Activity, diffusion, combination napmii
Activity, diffusion, combination napmni
Activity, diffusion, combination napmoi
Activity, diffusion, combination rsdh
Activity, diffusion, combination
Activity, diffusion, combination rsnh
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination ypltpmh
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, hpt
 combination, indicators (3)
Activity, diffusion, cumfg
 combination, indicators (2)
Activity, diffusion, lhelp
 combination, indicators (2)
Activity, diffusion, lr
 combination, indicators
Activity, indicators (2) napmvdi
Diffusion, combination cexp
Diffusion, combination lu0
Diffusion, combination lu15
Diffusion, combination lu5
Diffusion, combination luad
Diffusion, combination lut15
Diffusion, combination lut27
Diffusion, combination faram
Diffusion, combination faran
Diffusion, combination faranp
Diffusion, combination farat
Diffusion, combination farmsr
Diffusion, combination fm1
Diffusion, combination fm2c
Diffusion, combination fm3
Diffusion, combination (a) fxtwba
Diffusion, combination fxuk
Diffusion, combination faaa
Diffusion, combination fbaa
Diffusion, combination
Diffusion, combination
Diffusion, combination sdy5comm
Diffusion, combination sp500
Diffusion, combination spe5comm
Diffusion, combination spny
Diffusion, combination spspi
Diffusion, combination ftbs3
Diffusion, combination ftbs6
Diffusion, combination
Diffusion, combination
Diffusion, combination fcm1
Diffusion, combination fcm5
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination sp1000
Diffusion, combination sp3100
Diffusion, combination pcua
Diffusion, combination pcucc
Diffusion, combination pcuccd
Diffusion, combination pcucs
Diffusion, combination pcum
Diffusion, combination pcuslf
Diffusion, combination pcuslm
Diffusion, combination pcusls
Diffusion, combination pcut
Diffusion, combination jcdm
Diffusion, combination jcm
Diffusion, combination jcnm
Diffusion, combination jcsm
Diffusion, combination leconsa
Diffusion, combination lemanua
Diffusion, combination
Diffusion, combination, fm2
 indicators (5)
Diffusion, combination, fcm10
 indicators (5)
Diffusion, combination, ffed
 indicators
Diffusion, combination, sp2000
 indicators (4)
Diffusion, combination, sp3000
 indicators (4)
Diffusion, combination, napmpi
 indicators (4)
Indicators (1) log zlead
Indicators (3) log
Indicators (3) log hn1us
Indicators (1) log chm
Indicators (1) swxli2
Indicators (5) level
Indicatorsb (5) fxtwmb
Indicators (5)
Indicators (5)
Indicators (4) log pzall
Indicatorsc (3) log spwpcc
Indicators (4) log
Indicatorsd (4) log pzdalud
Indicators (4) log p101
Indicators (4) log ueg
Natural rate UGAP
Prices jcxfem

 Constructed series
Model mnemonic

Activity
Activity
Activity LCUN = a0m005
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination CONSTPV = cpv - cpvr
Activity, diffusion, combination CONSTPU = cpg
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination
Activity, diffusion, combination RSH = rsh + rsh2
Activity, diffusion, combination
Activity, diffusion, combination TIMDH = timdh + timdh2
Activity, diffusion, combination TIMH = timh + timh2
Activity, diffusion, combination TIMNH = timnh + timnh2
Activity, diffusion, combination TIRH = tirh + tirh2
Activity, diffusion, combination TITH = tith + tith2
Activity, diffusion, combination TIWH = tiwh + tiwh2
Activity, diffusion, combination TRMH = trmh + trmh2
Activity, diffusion, combination TRRH= trrh + trrh2
Activity, diffusion, combination TRTH= trth + trth2
Activity, diffusion, combination TRWMH=trwmh + trwmh2
Activity, diffusion, combination TSMDH= tsmdh + tsmdh2
Activity, diffusion, combination TSMH= tsmh + tsmh2
Activity, diffusion, combination TSMNH= tsmnh + tsmnh2
Activity, diffusion, combination TSTH= tsth + tsth2
Activity, diffusion, combination TSWMDH= tswmdh
Activity, diffusion, combination TSWMH= tswmh + twsmh2
Activity, diffusion, combination TSWMNH= tswmnh + tswmnh2
Activity, diffusion, combination
Activity, diffusion, combination CDVHM = cdvhm + cdvh
Activity, diffusion, combination MDOQ = a0m007
Activity, diffusion, combination MOCGMC = a0m008
Activity, diffusion, combination MOCNC = a0m027
Activity, diffusion,
 combination, indicators (3)
Activity, diffusion,
 combination, indicators (2)
Activity, diffusion,
 combination, indicators (2)
Activity, diffusion,
 combination, indicators
Activity, indicators (2)
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination (a)
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination DAAA = faaa - ffed
Diffusion, combination DBAA = fbaa -ffed
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination DTBS03 = ftbs3 - ffed
Diffusion, combination DTBS06 = ftbs6 - ffed
Diffusion, combination
Diffusion, combination
Diffusion, combination DCM1 = fmc1 - ffed
Diffusion, combination DCM5 = fmc5 -ffed
Diffusion, combination DCM10 = fcm10 -ffed
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination
Diffusion, combination FCLQ = a0m101
Diffusion, combination,
 indicators (5)
Diffusion, combination,
 indicators (5)
Diffusion, combination,
 indicators
Diffusion, combination,
 indicators (4)
Diffusion, combination,
 indicators (4)
Diffusion, combination,
 indicators (4)
Indicators (1) log
Indicators (3) log CPC = CONSTPV + CONSTPU
Indicators (3) log
Indicators (1) log
Indicators (1)
Indicators (5) level CM03CM01 = fcm3 - fmc1
Indicatorsb (5)
Indicators (5) PZGLD = pzgld + mgold + fgold
Indicators (5) PZSIL
Indicators (4) log
Indicatorsc (3) log
Indicators (4) log PFALL
Indicatorsd (4) log
Indicators (4) log
Indicators (4) log
Natural rate
Prices

Model Haver description

Activity Civilian employment: Sixteen years
 & over: 16 yr + (SA, 000s)
Activity Civilian unemployment rate: Men,
 25-54 years (SA, %)
Activity Average weekly initial claims
 unemployment insurance (SA, 000s)
Activity, diffusion, combination Personal consumption expenditures
 (SAAR, chained 2000$bil.)
Activity, diffusion, combination Personal consumption expenditures:
 Durable goods (SAAR, chained
 2000$bil.)
Activity, diffusion, combination Personal consumption expenditures:
 Nondurable goods (SAAR, chained
 2000$bil.)
Activity, diffusion, combination Personal consumption expenditures:
 Services (SAAR, chained 2000$bil.)
Activity, diffusion, combination Real disposable personal income
 (SAAR, chained 2000$bil.)
Activity, diffusion, combination Value of public construction put in
 place (SAAR, chained $mil.)
Activity, diffusion, combination Value of private construction put
 in place (SAAR, chained $mil.)
Activity, diffusion, combination Manufacturers' shipments of mobile
 homes (SAAR, units in 000s)
Activity, diffusion, combination Housing starts (SAAR, units in 000s)
Activity, diffusion, combination Housing starts: Midwest
 (SAAR, units in 000s)
Activity, diffusion, combination Housing starts: Northeast
 (SAAR, units in 000s)
Activity, diffusion, combination Housing starts: South (SAAR, units
 in 000s)
Activity, diffusion, combination Housing starts: West (SAAR, units
 in 000s)
Activity, diffusion, combination Industrial Production Index
 (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Consumer
 goods (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Durable
 consumer goods (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Nondurable
 consumer goods (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Business
 equipment (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Materials
 (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Durable
 goods materials (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Nondurable
 goods materials (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Nonindustrial
 supplies (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Mining
 (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Final
 products (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Durable
 goods [NAICS] (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Manufacturing
 [SIC] (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Nondurable
 manufacturing (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Final
 products and nonindustrial
 supplies (SA, 1997=100)
Activity, diffusion, combination Industrial Production: Electric and
 gas utilities (SA, 1997=100)
Activity, diffusion, combination All employees: Construction
 (SA, 000s)
Activity, diffusion, combination All employees: Durable goods
 manufacturing (SA, 000s)
Activity, diffusion, combination All employees: Financial activities
 (SA, 000s)
Activity, diffusion, combination All employees: Goods-producing
 industries (SA, 000s)
Activity, diffusion, combination All employees: Government (SA, 000s)
Activity, diffusion, combination All employees: Manufacturing
 (SA, 000s)
Activity, diffusion, combination All employees: Mining (SA, 000s)
Activity, diffusion, combination All employees: Total nonfarm
 (SA, 000s)
Activity, diffusion, combination All employees: Nondurable goods
 manufacturing (SA, 000s)
Activity, diffusion, combination All employees: Total private
 industries (SA, 000s)
Activity, diffusion, combination All employees: Retail trade
 (SA, 000s)
Activity, diffusion, combination All employees: Service-providing
 industries (SA, 000s)
Activity, diffusion, combination All employees: Aggregate of
 categories
Activity, diffusion, combination All employees: Aggregate of
 categories
Activity, diffusion, combination Civilian employment: Nonagricultural
 Industries: 16yr + (SA, 000s)
Activity, diffusion, combination Ratio: Help-wanted advertising in
 newspapers/Number unemployed (SA)
Activity, diffusion, combination Average weekly hours: Overtime:
 Manufacturing (SA, Hrs)
Activity, diffusion, combination Average weekly hours: Manufacturing
 (SA, Hrs)
Activity, diffusion, combination ISM Mfg: PMI Composite Index
 (SA, 50+ = Econ Expand)
Activity, diffusion, combination ISM Mfg: Employment Index
 (SA, 50+ = Econ Expand)
Activity, diffusion, combination ISM Mfg: Inventories Index
 (SA, 50+ = Econ Expand)
Activity, diffusion, combination ISM Mfg: New Orders Index
 (SA, 50+ = Econ Expand)
Activity, diffusion, combination ISM Mfg: Production Index
 (SA, 50+ = Econ Expand)
Activity, diffusion, combination Real retail sales: Durable goods
 (SA, chained 2000$mil.)
Activity, diffusion, combination Retail sales: Retail trade
 (SA, Spliced, chained 2000$mil.)
Activity, diffusion, combination Real retail sales: Nondurable goods
 (SA, chained 2000$mil.)
Activity, diffusion, combination Real inventories: Mfg: Durable goods
 industries (SA, EOP, spliced,
 chained 2000$mil.)
Activity, diffusion, combination Real manufacturing & trade
 inventories: Mfg industries (SA,
 EOP, spliced, chained 2000$mil.)
Activity, diffusion, combination Real mfg inventories: Nondurable
 goods industries (SA, EOP,
 spliced, chained 2000$mil.)
Activity, diffusion, combination Real inventories: Retail trade
 industries (SA, EOP, spliced,
 chained 2000$mil.)
Activity, diffusion, combination Real manufacturing & trade
 inventories: Industries (SA, EOP,
 spliced, chained 2000$mil.)
Activity, diffusion, combination Real inventories: Merchant wholesale
 trade industries (SA, EOP,
 spliced, chained 2000$mil.)
Activity, diffusion, combination Real inventories/sales ratio:
 Manufacturing industries
 (SA, spliced, chained 2000$)
Activity, diffusion, combination Inventories/sales ratio: Retail
 trade industries (SA, spliced,
 chained 2000$)
Activity, diffusion, combination Real manufacturing & trade:
 Inventories/sales ratio
 (SA, spliced, chained 2000$)
Activity, diffusion, combination Inventories/sales ratio: Merchant
 wholesale trade industries
 (SA, spliced, chained 2000$)
Activity, diffusion, combination Real sales: Mfg: Durable goods
 industries (SA, spliced, chained
 2000$mil.)
Activity, diffusion, combination Real sales: Manufacturing industries
 (SA, spliced, chained 2000$mil.)
Activity, diffusion, combination Real sales: Mfg: Nondurable goods
 industries (SA, spliced, chained
 2000$mil.)
Activity, diffusion, combination Real manufacturing & trade sales:
 All industries (SA, spliced,
 chained 2000$mil.)
Activity, diffusion, combination Real sales: Merchant wholesalers:
 Durable goods inds. (SA, spliced,
 chained 2000$mil.)
Activity, diffusion, combination Real sales: Merchant wholesale trade
 industries (SA, spliced, chained
 2000$mil.)
Activity, diffusion, combination Real sales: merchant wholesale:
 Nondurable goods inds. (SA,
 spliced, chained 2000$mil.)
Activity, diffusion, combination Real personal income less transfer
 payments (SAAR, chained 2000$bil.)
Activity, diffusion, combination PCE: Durable goods: Motor vehicles
 and parts (SAAR, spliced and
 interpolated, chained 2000$mil.)
Activity, diffusion, combination Manufacturers' new orders: Durable
 goods (SA, chained 2000$mil.)
Activity, diffusion, combination Manufacturers' new orders: Consumer
 goods & materials (SA, 1982$mil.)
Activity, diffusion, combination Manufacturers' new orders:
 Nondefense capital goods
 (SA, 1982$mil.)
Activity, diffusion, New private housing units
 combination, indicators (3) authorized by building permit
 (SAAR, units in 000s)
Activity, diffusion, Capacity utilization: Manufacturing
 combination, indicators (2) [SIC] (SA, % of capacity)
Activity, diffusion, Index of help-wanted advertising in
 combination, indicators (2) newspapers (SA, 1987=100)
Activity, diffusion, Civilian unemployment rate: 16yr +
 combination, indicators (SA, %)
Activity, indicators (2) ISM: Mfg: Vendor Deliveries Index
 (SA, 50+ = Econ Expand)
Diffusion, combination University of Michigan: Consumer
 expectations (NSA, 66Q1=100)
Diffusion, combination Civilians unemployed for less than
 5 weeks (SA, 000s)
Diffusion, combination Civilians unemployed for 15-26
 weeks (SA, 000s)
Diffusion, combination Civilians unemployed for 5-14 weeks
 (SA, 000s)
Diffusion, combination Average {Mean} duration of
 unemployment (SA, weeks)
Diffusion, combination Civilians unemployed for 15 weeks
 and over (SA, 000s)
Diffusion, combination Civilians unemployed for 27 weeks
 and over (SA, 000s)
Diffusion, combination Adjusted monetary base (SA, $mil.)
Diffusion, combination Adjusted nonborrowed reserves of
 depository institutions
 (SA, $mil.)
Diffusion, combination Adjusted nonborrowed reserves plus
 extended credit (SA, $mil.)
Diffusion, combination Adjusted reserves of depository
 institutions (SA, $mil.)
Diffusion, combination Adj. monetary base including
 deposits to satisfy clearing
 balance contracts (SA, $bil.)
Diffusion, combination Money stock: M1 (SA, $bil.)
Diffusion, combination Real money stock: M2 (SA, chained
 2000$bil.)
Diffusion, combination Money stock: M3 (SA, $bil.)
Diffusion, combination (a) Nominal broad trade-weighted
 exchange value of US$ (JAN 97=100)
Diffusion, combination Foreign exchange rate: United
 Kingdom (US$/Pound)
Diffusion, combination Moody's seasoned Aaa corporate bond
 yield (% p.a.)
Diffusion, combination Moody's seasoned Baa corporate bond
 yield (% p.a.)
Diffusion, combination Moody's seasoned Aaa corporate bond
 yield - fed funds rate(% p.a.)
Diffusion, combination Moody's seasoned Baa corporate bond
 yield - fed funds rate (% p.a.)
Diffusion, combination S&P: Composite 500, dividend yield
 (%)
Diffusion, combination Stock Price Index: Standard & Poor's
 500 Composite (1941-43=10)
Diffusion, combination S&P: 500 Composite, P/E ratio,
 4-qtr trailing earnings
Diffusion, combination Stock Price Index: NYSE Composite
 (Avg, Dec. 31, 2002=5000)
Diffusion, combination Stock Price Index: Standard & Poor's
 400 Industrials (1941-43=10)
Diffusion, combination 3-month Treasury bills, secondary
 market (% p.a.)
Diffusion, combination 6-month Treasury bills, secondary
 market (% p.a.)
Diffusion, combination 3-month Treasury bills - fed funds
 rate, (% p.a.)
Diffusion, combination 6-month Treasury bills - fed funds
 rate (% p.a.)
Diffusion, combination 1-year Treasury bill yield at
 constant maturity (% p.a.)
Diffusion, combination 5-year Treasury note yield at
 constant maturity (% p.a.)
Diffusion, combination 1-year Treasury bill yield at
 constant maturity - fed funds
 rate (% p.a.)
Diffusion, combination 5-year Treasury note yield at
 constant maturity - fed funds
 rate (% p.a.)
Diffusion, combination 10-year Treasury note yield at
 constant maturity - fed funds
 rate (% p.a.)
Diffusion, combination PPI: Crude materials for further
 processing (SA, 1982=100)
Diffusion, combination PPI: Finished consumer goods
 (SA, 1982=100)
Diffusion, combination CPI-U: Apparel (SA, 1982-84=100)
Diffusion, combination CPI-U: Commodities (SA, 1982-84=100)
Diffusion, combination CPI-U: Durables (SA, 1982-84=100)
Diffusion, combination CPI-U: Services (SA, 1982-84=100)
Diffusion, combination CPI-U: Medical care
 (SA, 1982-84=100)
Diffusion, combination CPI-U: All items less food
 (SA, 1982-84=100)
Diffusion, combination CPI-U: All items less medical care
 (SA, 1982-84=100)
Diffusion, combination CPI-U: All items less shelter
 (SA, 1982-84=100)
Diffusion, combination CPI-U: Transportation
 (SA, 1982-84=100)
Diffusion, combination PCE: Durable goods: Chain Price
 Index (SA, 2000=100)
Diffusion, combination PCE: Personal consumption
 expenditures: Chain Price Index
 (SA, 2000=100)
Diffusion, combination PCE: Nondurable goods: Chain Price
 Index (SA, 2000=100)
Diffusion, combination PCE: Services: Chain Price Index
 (SA, 2000=100)
Diffusion, combination Avg hourly earnings: Construction
 (SA, $/Hr)
Diffusion, combination Avg hourly earnings: Manufacturing
 (SA, $/Hr)
Diffusion, combination Commercial & industrial loans
 outstanding (EOP, SA, chained
 2000$mil.)
Diffusion, combination, Money stock: M2 (SA, $bil.)
 indicators (5)
Diffusion, combination, 10-year Treasury note yield at
 indicators (5) constant maturity (% p.a.)
Diffusion, combination, Federal funds [effective] rate
 indicators (% p.a.)
Diffusion, combination, PPI: Intermediate materials,
 indicators (4) supplies, and components
 (SA, 1982=100)
Diffusion, combination, PPI: Finished goods (SA, 1982=100)
 indicators (4)
Diffusion, combination, ISM: Mfg: Prices Index (NSA, 50+ =
 indicators (4) Econ Expand)
Indicators (1) log Composite Index of 10 Leading
 Indicators (1996=100)
Indicators (3) log New construction put in place
 (SAAR, 2000$mil.)
Indicators (3) log New single-family houses sold:
 United States (SAAR, 000s)
Indicators (1) log Personal consumption expenditures
 (SAAR, chained 2000$mil.)
 (spliced from usna96 before 1990)
Indicators (1) Stock and Watson nonfinancial
 leading index %
Indicators (5) level 3-year/1-year T-bill spread
Indicatorsb (5) Nominal trade-weighted exch value of
 US$/major currencies (MAR 73=100)
Indicators (5) Cash prices: gold, Handy & Harman
 Base Price (avg, spliced,
 $/Troy oz)
Indicators (5) Cash price: silver, troy oz, Handy
 & Harman Base Price
 (avg, $/troy oz)
Indicators (4) log KR-CRB Spot Commodity Price Index:
 All commodities
Indicatorsc (3) log SPOT COMMODITY PRICE - PLYWOOD,
 CROWS (PUIWMWPC_N.WT)
Indicators (4) log KR-CRB Futures: All commodities
 (avg, 1967=100) weekly
Indicatorsd (4) log Aluminum ingot producer price:
 Delivered Midwest (avg, cents/lb)
Indicators (4) log PPI: Iron and steel (NSA, 1982=100)
Indicators (4) log CPI-U: Energy (SA, 1982-84=100)
Natural rate Unemployment gap constructed from
 Perry-weighted unemployment rate
Prices PCE less food and energy: Price
 Index (SA) (2000=100)

 Haver Secondary
Model database source

Activity usecon
Activity usecon
Activity bci
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usecon
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usna
Activity, diffusion, combination usecon
Activity, diffusion, combination usna
Activity, diffusion, combination bci
Activity, diffusion, combination bci
Activity, diffusion, combination bci
Activity, diffusion, usecon
 combination, indicators (3)
Activity, diffusion, usecon
 combination, indicators (2)
Activity, diffusion, usecon
 combination, indicators (2)
Activity, diffusion, usecon
 combination, indicators
Activity, indicators (2) usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination (a) usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination usna
Diffusion, combination usna
Diffusion, combination usna
Diffusion, combination usna
Diffusion, combination usecon
Diffusion, combination usecon
Diffusion, combination bci
Diffusion, combination, usecon
 indicators (5)
Diffusion, combination, usecon
 indicators (5)
Diffusion, combination, usecon
 indicators
Diffusion, combination, usecon
 indicators (4)
Diffusion, combination, usecon
 indicators (4)
Diffusion, combination, usecon
 indicators (4)
Indicators (1) log bci
Indicators (3) log usecon
Indicators (3) log usecon
Indicators (1) log usna
Indicators (1) usecon
Indicators (5) level usecon
Indicatorsb (5) usecon
Indicators (5) weekly COMEX, FSC
Indicators (5) weekly FSC
Indicators (4) log usecon
Indicatorsc (3) log FAME
Indicators (4) log BCRB
Indicatorsd (4) log weekly
Indicators (4) log usecon
Indicators (4) log cpidata
Natural rate empl
Prices usna

COMEX http://www.wrenresearch.com.au/downloads/index.htm
FSC http://www.webspace4me.net/~blhill2/data/commodities
BCRB http://economic-charts.com/em-cgi/data.exe/crb/crb01
FAME Federal Reserve Bank of San Francisco website

(a) fxtwb begins in 1973:01

(b) fxtwm begins in 1973:01

(c) cspwpc begins in 1979:01

(d) pzdalu begins in 1988:07

Indicator model groups:

(1:) Economic activity

(2:) Slackness measures

(3:) Housing and building activity

(4:) Industrial prices

(5:) Financial markets

Notes: SAAR is seasonally adjusted annual rate, SA is seasonally
adjusted, NSA is not seasonally adjusted, NAICS is North American
industry classification system, SIC is standard industrial
classification, and EOP is end of period.

DATA APPENDIX

Quarterly data: 1967:1-2003:4

Model Transformation Mnemonic

Activity log 1st diff ch
Activity log 1st diff cdh
Activity log 1st diff cnh
Activity log 1st diff csh
Activity log 1st diff ih
Activity log 1st diff fh
Activity log 1st diff fnsh
Activity log 1st diff fneh
Activity 1st diff vh
Activity 1st diff xneth
Activity log 1st diff gh
Activity log 1st diff gfnh
Activity log 1st diff ypdh
Activity log 1st diff gdpbq
Activity log 1st diff fsq
Activity, Indicators (1) log 1st diff gdph
Activity, Indicators (3) log 1st diff fnh
Activity, Indicators (3) log 1st diff frh
Diffusion, Combination log 1st diff lxba
Diffusion, Combination log 1st diff lxbc
Diffusion, Combination log 1st diff lxbr
Diffusion, Combination log 1st diff lxbu
Diffusion, Combination log 1st diff lxbn
Diffusion, Combination log 1st diff lxnfn
Diffusion, Combination log 1st diff lxma
Diffusion, Combination log 1st diff lxmda
Diffusion, Combination log 1st diff lxmna
Diffusion, Combination log 1st diff lxnca
Diffusion, Combination log 1st diff lxncc
Diffusion, Combination log 1st diff lxncr
Diffusion, Combination log 1st diff lxncu
Diffusion, Combination log 1st diff lxncn
Diffusion, Combination log 1st diff lxnct
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff
Diffusion, Combination log 1st diff grt
Diffusion, Combination log 1st diff get
Diffusion, Combination 1st diff gnl
Diffusion, Combination log 1st diff dgdp
Diffusion, Combination log 1st diff di
Diffusion, Combination log 1st diff df
Diffusion, Combination log 1st diff dfn
Diffusion, Combination log 1st diff dfns
Diffusion, Combination log 1st diff dfne
Diffusion, Combination log 1st diff dfr
Diffusion, Combination log 1st diff dg
Diffusion, Combination log 1st diff dgfn
Diffusion, Combination log 1st diff dm
Diffusion, Combination log 1st diff dx
Diffusion, Combination, log 1st diff lxnfa
 Indicators (6)
Diffusion, Combination, log 1st diff lxnfc
 Indicators (6)
Diffusion, Combination, log 1st diff lxnfr
 Indicators (6)
Diffusion, Combination, log 1st diff lxnfu
 Indicators (6)
Diffusion, Combination, log 1st diff
 Indicators (6)
Output Gap band-pass filtered
Real Unit Labor Cost Gap band-pass filtered
Prices log 2nd diff jcxfe

 Constructed series
Model mnemonic

Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity
Activity, Indicators (1)
Activity, Indicators (3)
Activity, Indicators (3)
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination BRULC= lxbu/lxbi
Diffusion, Combination FRULC= lnxncu/lxnci
Diffusion, Combination BNLRULC= lxbn/lxbi
Diffusion, Combination NFNLRULC = lxnfn/lxnfi
Diffusion, Combination FNLRULC= lxncn/lxnci
Diffusion, Combination FTOTRUC= lnxnct/lxnci
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination
Diffusion, Combination,
 Indicators (6)
Diffusion, Combination,
 Indicators (6)
Diffusion, Combination,
 Indicators (6)
Diffusion, Combination,
 Indicators (6)
Diffusion, Combination, NFRULC= lxnfu/lxnfi
 Indicators (6)
Output Gap OGAP
Real Unit Labor Cost Gap RGAP
Prices

Model Haver description

Activity Real Personal Consumption Expenditures
 (SAAR, Bil. Chn. 2000 $)
Activity Real Personal Consumption Expenditures:
 Durable Goods (SAAR, Bil. Chn. 2000 $)
Activity Real Personal Consumption Expenditures:
 Non-Durable Goods (SAAR, Bil. Chn. 2000 $)
Activity Real Personal Consumption Expenditures:
 Services (SAAR, Bil. Chn. 2000 $)
Activity Real Gross Private Domestic Investment
 (SAAR, Bil. Chn. 2000 $)
Activity Real Private Fixed
Activity Real Private Nonresidential Structures
Activity Real Private Nonresidential Equipment &
 Software
Activity Real Change in Private Inventories (SAAR,
 Bil. Chn. 2000 $)
Activity Real Net Exports of Goods & Services
 (SAAR, Bil. Chn. 2000 $)
Activity Real Govt. Consumption Expenditures & Gross
 Investment (SAAR, Bil. Chn. 2000 $)
Activity Real Govt. Non-defense Consumption
 Expenditures & Gross Investment
 (SAAR, Bil. Chn. 2000 $)
Activity Real Disposable Personal Income
 (SAAR, Bil. Chn. 2000 $)
Activity Index of Business Gross Value added
Activity Index of Real Final Sales
Activity, Indicators (1) Real Gross Domestic Product
 (SAAR, Bil. Chn. 2000 $)
Activity, Indicators (3) Real Private Nonresidential
Activity, Indicators (3) Real Private Residential
Diffusion, Combination Business Sector: Output per Hour of all
 Persons (SA, 1992=100)
Diffusion, Combination Business Sector: Compensation per Hour of
 all Persons (SA, 1992=100)
Diffusion, Combination Business Sector: Real Compensation per Hour
 of all Persons (SA, 1992=100)
Diffusion, Combination Business Sector: Unit Labor Costs
 (SA, 1992=100)
Diffusion, Combination Business Sector: Unit Non-Labor Payments
 (SA, 1992=100)
Diffusion, Combination Non-farm Business Sector: Unit Non-Labor
 Payments (SA, 1992=100)
Diffusion, Combination Manufacturing Sector: Output per Hour of
 all Persons (SA, 1992=100)
Diffusion, Combination Manufacturing Sector Durables: Output per
 Hour of all Persons (SA, 1992=100)
Diffusion, Combination Manufacturing Sector Non-durables: Output
 per Hour of all Persons (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Output per
 Hour, All employees (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Compensation
 per Hour, All employees (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Real
 Compensation per Hour, All employees
 (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Unit Labor
 Costs, All employees (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Unit Non-Labor
 Costs, All employees (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Total Unit
 Costs, All employees (SA, 1992=100)
Diffusion, Combination Business Sector: Real Unit Labor Costs
 (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Real Unit Labor
 Costs, All employees (SA, 1992=100)
Diffusion, Combination Business Sector: Real Unit Non-Labor
 Payments (SA, 1992=100)
Diffusion, Combination Non-farm Business Sector: Real Unit
 Non-Labor Payments (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Real Unit
 Non-Labor Costs, All employees
 (SA, 1992=100)
Diffusion, Combination Non-financial Corporations: Real Total Unit
 Costs, All employees (SA, 1992=100)
Diffusion, Combination Government Total Receipts (SAAR, Bil. $)
Diffusion, Combination Government Total Expenditures (SAAR, Bil. $)
Diffusion, Combination Government Net Lending or Net Borrowing
 (SAAR, Bil. $)
Diffusion, Combination GDP Deflator
Diffusion, Combination Gross Private Domestic Investment: Implicit
 Price Deflator (SA, 2000=100)
Diffusion, Combination Private Fixed Investment: Implicit Price
 Deflator (SA, 2000=100)
Diffusion, Combination Private Non-residential Fixed Investment:
 Implicit Price Deflator (SA, 2000=100)
Diffusion, Combination Private Non-residential Structures:
 Implicit Price Deflator (SA, 2000=100)
Diffusion, Combination Private Non-residential Equipment/Software:
 Implicit Price Deflator (SA, 2000=100)
Diffusion, Combination Private Residential Investment: Implicit
 Price Deflator (SA, 2000=100)
Diffusion, Combination Government Consumption/Gross Investment:
 Implicit Price Deflator (SA, 2000=100)
Diffusion, Combination Federal Non-Defense Consumption/Investment:
 Implicit Price Deflator (SA, 2000=100)
Diffusion, Combination Imports of Goods & Services: Implicit Price
 Deflator (SA, 2000=100)
Diffusion, Combination Exports of Goods & Services: Implicit Price
 Deflator (SA, 2000=100)
Diffusion, Combination, Non-farm Business Sector: Output per Hour
 Indicators (6) of all Persons (SA, 1992=100)
Diffusion, Combination, Non-farm Business Sector: Compensation per
 Indicators (6) Hour of all Persons (SA, 1992=100)
Diffusion, Combination, Non-farm Business Sector: Real Compensation
 Indicators (6) per Hour of all Persons (SA, 1992=100)
Diffusion, Combination, Non-farm Business Sector: Unit Labor Costs
 Indicators (6) (SA, 1992=100)
Diffusion, Combination, Non-farm Business Sector: Real Unit Labor
 Indicators (6) Costs (SA, 1992=100)
Output Gap Output gap constructed from band-pass
 filtered Real GDP
Real Unit Labor Cost Gap Band-pass filtered version of Non-farm
 Business Sector Real Unit Labor Costs
Prices PCE less food and Energy: Price Index (SA)
 (2000=100)

 Haver
Model database

Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity usna
Activity, Indicators (1) usna
Activity, Indicators (3) usna
Activity, Indicators (3) usna
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usecon
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination usna
Diffusion, Combination, usecon
 Indicators (6)
Diffusion, Combination, usecon
 Indicators (6)
Diffusion, Combination, usecon
 Indicators (6)
Diffusion, Combination, usecon
 Indicators (6)
Diffusion, Combination, usecon
 Indicators (6)
Output Gap usna
Real Unit Labor Cost Gap usecon
Prices usna

Indicator Model Groups:

(1:) Economic Activity

(2:) Slackness Measures

(3:) Housing and Building Activity

(4:) Industrial Prices

(5:) Financial Markets

(6:) Productivity and Marginal Cost

REFERENCES

Atkeson, Andrew, and Lee E. Ohanian, 2001, "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, Vol. 25, No. 1, Winter, pp. 2-11.

Cecchetti, Stephen G., Rita S. Chu, and Charles Steindel, 2000, "The unreliability of inflation indicators," Current Issues in Economics and Finance, April, Vol. 6, No. 4.

Christiano, Lawrence J., and Terry Fitzgerald, 1999, "The band-pass filter," National Bureau of Economic Research, working paper, No. 7257, July.

Clark, Todd E., and Michael W. McCracken, 2004, "The predictive content of the output gap for inflation: Resolving in-sample and out-of-sample evidence," manuscript.

--, 2001, "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Vol. 105, November, pp. 85-110.

Fisher, Jonas D. M., Chin Liu, and Ruilin Zhou, 2002, "When can we forecast inflation?," Economic Perspectives, Federal Reserve Bank of Chicago, First Quarter, pp. 30-42.

Marcellino, Massimiliano, James H. Stock, and Mark Watson, 2004, "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," manuscript.

Sargent, Thomas, 1999, The Conquest of American Inflation, Princeton, NJ: Princeton University Press.

Sims, Christopher, 2002, "The role of models and probabilities in the monetary policy process," Brookings Papers on Economic Activity, Vol. 2, pp.1-62.

Stock, James H., and Mark Watson, 2003, "Forecasting output and inflation: The role of asset prices," Journal of Economic Literature.

--, 2002, "Macroeconomic forecasting using diffusion indexes," Journal of Business and Economic Statistics, Vol. 20, No. 2, April, pp. 147-162.

--, 1999, "Forecasting inflation," Journal of Monetary Economics, Vol. 44, No. 2.

NOTES

(1) See, for example, Sims (2002) and Stock and Watson (2002). Fisher, Liu, and Zhou (2002) document that the failure of Phillips curve models after 1985 is essentially due to an especially poor performance in the 1985-92 period.

(2) One might view equation 1 as an odd choice to base inflation forecasts on since it involves changes of inflation rather than levels of inflation. The reason we use this equation is because it performs better than models based on the level of inflation. This reflects the fact that 12-month inflation is an extremely persistent variable, so that its level does not change much over short periods.

(3) Specifically, we use the Bayes information criterion (BIC) to select the number of lags. Intuitively, BIC selects the number of lags to improve the fit of the model without increasing by too much the sampling error in the lag coefficients.

(4) Another way to forecast inflation would be to formulate a vector autoregression in the level or change in one-month inflation and the indicator variables and project this system forward J periods from date T. Such a forecast would yield superior results if the vector autoregression were correctly specified. The conventional wisdom is that the direct approach taken here is in practice better. Marcellino, Stock, and Watson (2004) show that for many variables, but not for inflation, this conventional wisdom is apparently false. We have explored the "multi-step iterated forecasts" described in Marcellino, Stock, and Watson (2004) and concur with their finding that this approach is a poor forecasting strategy for inflation.

(5) To estimate the natural rate, we use a filter applied to the time series of unemployment available at the time of the forecast. The particular filter we use is called a band-pass filter. This is designed to isolate particular frequencies of the data. We use it to isolate "long-run" or low frequency fluctuations in the unemployment rate. Specifically, we focus on fluctuations of period (inversely related to the frequency) 12 years or greater. The particular implementation of the band-pass filter we use is the one due to Christiano and Fitzgerald (1999).

(6) The index methodology was proposed by Stock and Watson (1999, 2002). For more details on the CFNAI, see www.chicagofed.org/ economic_research_and_data/cfnai.cfm.

(7) Technically, we compute the first six principal components of the 145 variables.

(8) The median of six forecasts is the average of the third and fourth ranked forecasts. We explored other ways of choosing among the six models, including using the mean and using the best out-of-sample forecasting performance (this is described later) up to the date of the forecast. These other ways of summarizing the forecasts performed similarly to the approach taken here.

(9) The word "meta" is often used to describe an analysis that synthesizes research results obtained using different approaches to a question. By this definition, the diffusion, combination, and indicator models might also be considered meta models. We prefer not to use this descriptor to classify these models since they combine the information from forecasts that, except for the indicators used, are based on the same forecasting strategy.

(10) We use this measure of inflation since it plays a prominent role in FOMC discussions.

(11) Compiling the data that were available at a particular point in time is a daunting task. A real-time dataset is available from the Philadelphia Fed. Unfortunately this dataset has a limited number of variables and excludes many that might be useful for forecasting inflation.

(12) Data revisions are a problem for the naive and autoregression models since the price index we use, the PCE deflator, is subject to revisions.

(13) Comparisons of models based on RMSE are subject to sampling variability and consequently subject to error. In principle, we could use Monte Carlo methods to assess the magnitude of this error. However, this would require specifying an underlying data-generating process for all the variables in our analysis (more than 150 of them). This sampling error should be kept in mind when interpreting the results. See Clark and McCracken (2001) and the references they cite for a useful discussion of some of the issues involved in assessing the statistical difference in the accuracy of forecasts.

(14) For another discussion of this point, see Cecchetti, Chu, and Steindel (2000).

(15) In principle there is nothing wrong with a negative weight. Conditional on all the other forecasts, a forecast of an increase in inflation from a model with a negative weight is a signal that the other models combined are forecasting an increase in inflation that is too big or a decrease in inflation that is not big enough, relative to past experience. If the model did not provide information about inflation, then it would get a zero weight.

(16) When computing the weighted forecasts at the quarterly horizon, we add the forecasts of the output gap model to the list of forecasts that are averaged.

(17) We also examine the impact of just averaging the monthly data to convert it to the quarterly frequency. When we do this, we find little evidence that monthly noise is a significant source of forecast error since there is not a consistent pattern of improvement in the quarterly models and when there is improvement it is typically much less than one-tenth of a percentage point.

(18) Another important caveat involves the use of rolling regressions. Sargent (1999) argues that the rise of inflation during the 1960s and 1970s and the subsequent decline can be explained by a process of the Fed learning and forgetting about its ability to exploit a perceived trade-off between inflation and unemployment. This analysis suggests a potential problem with using the rolling regression framework, because it may lead to a recurrence of the rise of inflation in the 1960s and 1970s. However, as Sargent (1999, p. 134) points out, a credible commitment by the Fed to low inflation should prevent such a recurrence. Under this view, there is no problem with using the rolling regression approach to forecasting.

(19) See Clark and McCracken (2004) for a recent analysis of the predictive content of the output gap for inflation.

Scott Brave is an associate economist and Jonas D. M. Fisher is an economic advisor at the Federal Reserve Bank of Chicago. The authors thank Craig Furfine and Marcelo Veracierto for helpful comments.

TABLE 1
Summary of models

Model Estimation equation Indicators used

Naive [[pi].sup.12.sub.t+J] - None
 [[pi].sup.12.sub.t] =
 [[epsilon].sub.t+J]

Autoregression [[pi].sup.12.sub.t+J] - None
 [[pi].sup.12.sub.t] = [alpha]
 + [beta](L)([[pi].sub.t] -
 [[pi].sub.t-1]) +
 [[epsilon].sub.t+J]

Natural rate [[pi].sup.12.sub.t+J] - Filtered
 [[pi].sup.12.sub.t] = [alpha] unemployment rate
 + [beta](L)([[pi].sub.t]
 - [[pi].sub.t-1]) +
 [[theta].sub.1](L)[x.sub.1t] +
 [[epsilon].sub.t+J]

Output gap [[pi].sup.12.sub.t+J] - Filtered real GDP
 [[pi].sup.12.sub.t] = [alpha]
 + [beta](L)([[pi].sub.t] -
 [[pi].sub.t-1]) +
 [[theta].sub.1](L)[x.sub.1t] +
 [[epsilon].sub.t+J]

Activity [[pi].sup.12.sub.t+J] - Index based on
 [[pi].sup.12.sub.t] = [alpha] indicators listed
 + [beta](L)([[pi].sub.t] - in appendix
 [[pi].sub.t-1]) +
 [[summation].sup.3.sub.i=1]
 [[theta].sub.i](L)[x.sub.it]
 + [[epsilon].sub.t+J]

Indicator [[pi].sup.12.sub.t+J] - Change in fed funds
 [[pi].sup.12.sub.t] = [alpha] rate, unemployment
 + [beta](L)([[pi].sub.t] - rate, indicators
 [[pi].sub.t-1]) + listed in appendix
 [[theta].sub.1](L)[x.sub.1t] +
 [[epsilon].sub.t+J]

Combination [[pi].sup.12.sub.t+J] - Indicators listed in
 [[pi].sup.12.sub.t] = [alpha] appendix
 + [beta](L)([[pi].sub.t] -
 [[pi].sub.t-1]) +
 [[theta].sub.1](L)[x.sub.1t] +
 [[epsilon].sub.t+J]

Diffusion [[pi].sup.12.sub.t+J] - Six indexes based on
 [[pi].sup.12.sub.t] = [alpha] indicators listed in
 + [beta](L)([[pi].sub.t] - appendix
 [[pi].sub.t-1]) +
 [[K.summation over (i=1)]
 [[theta].sub.i](L)[x.sub.it] +
 [[epsilon].sub.t+J],
 K = 1,2, ..., 6

Notes: See the text for a description of the notation and terminology.
NA denotes not applicable; GDP denotes gross domestic product.

TABLE 2

Top five indicators, various sample periods:
Combination and indicator variables

A. One-year ahead forecasts

1977-84
ISM: Mfg: Prices Index
Real inventories: Mfg: Durable goods industries
Housing starts: Northeast
ISM: Mfg: Inventories Index
ISM: Mfg: Supplier Delivery Index

1985-92
Housing starts: Midwest
NBER XLI2
Gold prices
Silver prices
CRB Futures Index

1993-2000
Civilians unemployed for 5-14 weeks
Housing starts
3-year/1-year T-bill spread
10-Year Treasury note yield - federal funds rate
Civilians unemployed for 15-26 weeks

2001-03
Civilians unemployed for 27 weeks and over
Average duration of unemployment
Civilians unemployed for 15 weeks and over
Civilians unemployed for 5-14 weeks
10-Year Treasury note yield - federal funds rate

B. Two-year ahead forecasts

1977-84
ISM Mfg: PMI Composite Index
ISM: Mfg: Supplier Delivery Index
ISM: Mfg: Inventories Index
ISM: Mfg: Employment Index
Housing starts: Midwest

1985-92
Housing starts: Midwest
Civilians unemployed for 15-26 weeks
Gold prices
Silver prices
New home sales

1993-2000
Civilians unemployed for 5-14 weeks
Housing starts
Civilians unemployed for 15-26 weeks
Housing starts: South
Building permits

2001-03
Civilians unemployed for 5-14 weeks
Civilian unemployment rate: 16yr+
Employment retail and wholesale trade
Industrial Production Index
Civilians unemployed for 15-26 weeks

TABLE 3
Monthly RMSE ranking, including meta and rolling models:
One-year and two-year ahead forecasts

A. 1-year ahead forecasts 1977-84
 Natural rate
 Equally weighted
 Rolling equally weighted
 Naive
 Activity
 Indicators
 Combination
 Autoregression
 Diffusion
 Natural

Summary statistics
Best RMSE 1.03
Worst RMSE - Best RMSE 0.49
[absolute value of Naive RMSE - Best RMSE] 0.20
Average inflation 6.48

B. 2-year ahead forecasts 1977-84
 Rolling equally weighted
 Equally weighted
 Diffusion
 Naive
 Natural rate
 Activity
 Combination
 Autoregression
 Indicators

Summary statistics
Best RMSE 1.62
Worst RMSE - Best RMSE 1.32
[absolute value of Naive RMSE - Best RMSE] 0.50
Average inflation 6.48

A. 1-year ahead forecasts 1985-92
 Optimally weighted
 Rolling equally weighted
 Rolling optimally weighted
 Naive
 Equally weighted
 Combination
 Autoregression
 Indicators
 Diffusion
 Rate
 Activity

Summary statistics
Best RMSE 0.50
Worst RMSE - Best RMSE 0.39
[absolute value of Naive RMSE - Best RMSE] 0.02
Average inflation 3.84

B. 2-year ahead forecasts 1985-92
 Rolling equally weighted
 Rolling optimally weighted
 Naive
 Diffusion
 Optimally weighted
 Equally weighted
 Combination
 Autoregression
 Indicators
 Activity
 Natural rate

Summary statistics
Best RMSE 0.60
Worst RMSE - Best RMSE 0.87
[absolute value of Naive RMSE - Best RMSE] 0.12
Average inflation 3.84

A. 1-year ahead forecasts 1993-2000
 Rolling optimally weighted
 Rolling equally weighted
 Optimally weighted
 Equally weighted
 Diffusion
 Naive
 Activity
 Natural rate
 Combination
 Autoregression
 Indicators

Summary statistics
Best RMSE 0.33
Worst RMSE - Best RMSE 0.23
[absolute value of Naive RMSE - Best RMSE] 0.11
Average inflation 1.87

B. 2-year ahead forecasts 1993-2000
 Optimally weighted
 Rolling optimally weighted
 Rolling equally weighted
 Equally weighted
 Diffusion
 Activity
 Naive
 Indicators
 Combination
 Natural rate
 Autoregression

Summary statistics
Best RMSE 0.39
Worst RMSE - Best RMSE 0.45
[absolute value of Naive RMSE - Best RMSE] 0.35
Average inflation 1.87

A. 1-year ahead forecasts 2001-03
 Rolling optimally weighted
 Optimally weighted
 Natural rate
 Rolling equally weighted
 Equally weighted
 Naive
 Combination
 Autoregression
 Diffusion
 Indicators
 Activity

Summary statistics
Best RMSE 0.38
Worst RMSE - Best RMSE 0.29
[absolute value of Naive RMSE - Best RMSE] 0.12
Average inflation 1.57

B. 2-year ahead forecasts 2001-03
 Equally weighted
 Natural rate
 Rolling optimally weighted
 Optimally weighted
 Combination
 Rolling equally weighted
 Naive
 Autoregression
 Indicators
 Diffusion
 Activity

Summary statistics
Best RMSE 0.30
Worst RMSE - Best RMSE 0.47
[absolute value of Naive RMSE - Best RMSE] 0.25
Average inflation 1.57

A. 1-year ahead forecasts 1985-2003
 Rolling optimally weighted
 Rolling equally weighted
 Optimally weighted
 Equally weighted
 Naive
 Combination
 Autoregression
 Diffusion
 Natural rate
 Indicators
 Activity

Summary statistics
Best RMSE 0.42
Worst RMSE - Best RMSE 0.28
[absolute value of Naive RMSE - Best RMSE] 0.06
Average inflation 2.65

B. 2-year ahead forecasts 1985-2003
 Rolling equally weighted
 Rolling optimally weighted
 Optimally weighted
 Diffusion
 Naive
 Equally weighted
 Combination
 Autoregression
 Indicators
 Activity
 Natural rate

Summary statistics
Best RMSE 0.54
Worst RMSE - Best RMSE 0.57
[absolute value of Naive RMSE - Best RMSE] 0.16
Average inflation 2.65

Notes: RMSE is root mean-squared error. Meta models are in bold above
and include the following individual models: naive, activity,
diffusion, combination, natural rate, and indicators.