Economics Group. Special Commentary. October 25, 2018

Transcription

1 Economics Group Special Commentary Azhar Iqbal, Econometrician (70) Finding Dory: A New Framework to Estimate the Natural Unemployment Rate There is nothing either good or bad but thinking makes it so. William Shakespeare Executive Summary Recent remarks by Federal Reserve Chair Jerome Powell highlight the importance of the natural unemployment rate for monetary policy decision-making, while acknowledging the uncertainty around existing estimates. 1 Because full employment is one of the goals of the Federal Reserve, an accurate measure of the natural unemployment rate would help the Federal Open Market Committee (FOMC) select an appropriate policy stance. If the unemployment rate is above the projected natural rate, the FOMC would want to maintain an accommodative policy stance to stimulate the economy and thereby bring down the unemployment rate. However, finding a realtime accurate measure of the natural unemployment rate is rather difficult because that rate depends on the current state of the economy, which is constantly evolving. In other words, finding an accurate measure of the natural unemployment rate, in real time, is akin to finding Dory (a fish) in the ocean. In this report, which is full of technical details, we present a new methodology for estimating the natural unemployment rate, which we refer to as the u-optimal rate. Our method is an alternative to the non-accelerating inflation rate of unemployment, or NAIRU, which is widely utilized as a gauge for the natural unemployment rate. However, the relationship between macroeconomic variables, such as the unemployment rate and inflation, changes over time, causing estimates of the natural rate based on traditional methods, such as the Phillips Curve, to be imprecise in guiding monetary policy. Our approach is more flexible because it incorporates the evolving nature of the economy when estimating the natural rate of unemployment. Utilizing inflation and growth expectations as inputs, while applying different time-varying weights to these variables, our approach has some major benefits over traditional methods. More precisely, we construct the u-optimal rate using our estimates of the six-month ahead probabilities of three different inflation scenarios (inflationary pressure, deflationary pressure and stable prices) and three different growth scenarios (recession, weakening pace of expansion and strengthening pace of expansion). Our model also accounts for structural breaks in the Phillips Curve, which academic research suggests are a result of demographic and productivity dynamics influencing the natural unemployment rate. 2 We suggest that our approach to estimating the natural rate of unemployment is more effective than traditional methods, and that it would help policymakers gauge the appropriate stance of monetary policy. This report presents our methodology for estimating the u-optimal rate. We will discuss implications for monetary policy from our analysis in this technical report in a follow-up non-technical report. An accurate measure of the natural unemployment rate would help the FOMC. 1 Powell, Jerome H. Monetary Policy in a Changing Economy. August 2, Ball, Laurence and N. Gregory Mankiw. (2002). The NAIRU in Theory and Practice. Journal of Economic Perspectives. Vol 1, No. This report is available on wellsfargo.com/economics and on Bloomberg WFRE.

2 The widely utilized benchmark to gauge the natural unemployment rate is the NAIRU. The u- optimal rate should not be a constant estimate, but should be a timevarying measure. Re-evaluating the Benchmark: The NAIRU and the Phillips Curve The widely utilized benchmark to gauge the natural unemployment rate is the non-accelerating inflation rate of unemployment (NAIRU). The Fed refers to the natural rate of unemployment as u* (u star). If the unemployment rate is above the natural rate then that is an indication of labor market slack, and the FOMC would want to maintain an accommodative policy stance in an attempt to bring down the unemployment rate. An unemployment rate below the natural rate, however, would suggest a risk of an overheating economy and rising inflation. In that scenario, the Fed would want to remove policy accommodation via rate hikes in order to slow growth. One of the most widely known methods of estimating the natural unemployment rate is the Phillips Curve. The Phillips Curve exhibits a tradeoff (negative relationship) between the unemployment rate and inflation, meaning that a lower unemployment rate is associated with higher inflation and vice versa. However, the U.S. economy suffered from a high unemployment rate along with high (double-digit) inflation during the 1970s, which raised doubts about the reliability of the Phillips Curve. This concern has been extensively debated in academic research. Ball and Mankiw (2002) suggested that expected inflation could cause a shift in the Phillips Curve (change the strength of the relation between inflation and the unemployment rate), and therefore, a measure of expected inflation would improve a model s fit, or accuracy. By suggesting a structural break in the Phillips Curve, Ball and Mankiw suggested that demographics and productivity factors influence the natural unemployment rate, and must be included to incorporate the break. Staiger, Stock and Watson (1997), on the other hand, suggested the NAIRU had a wider band (upper and lower limit), which reduces the effectiveness of the NAIRU as a proxy for the natural rate of unemployment. They estimated the NAIRU in 1990 was.2% with a range from.1% to 7.7%. More recently, Powell (2018) suggested the real-time estimates of longer-run economic variables are prone to error, since they cannot be directly observed. For instance, observers in the mid-190s through the 1980s in retrospect significantly under-estimated the natural unemployment rate, but they subsequently significantly over-estimated it in the 1990s. A New Method to Estimate the U-Optimal Our approach utilizes probabilities of the growth and inflation outlooks to estimate the natural unemployment rate, or what we refer to as u-optimal. For example, different growth outlooks (a weaker vs. stronger recovery) would affect the unemployment rate (rising vs. declining unemployment), all else equal. Similarly, different inflation regimes (inflationary vs. deflationary pressure) would assign a different natural rate of unemployment to different periods. Given the evolving nature of the economy, the u-optimal rate should not be a constant estimate, but should be a time-varying measure to capture different growth/inflation regimes. Following the research of Ball and Mankiw, we include probabilities of the inflation outlook to capture near-term inflation expectations. As the near-term growth outlook affects the unemployment rate, we also include probabilities of the growth outlook in our model. Because Ball and Mankiw suggested demographic and productivity dynamics are the potential source of a structural break in the inflation/unemployment relation, we have incorporated the labor force participation rate (to capture demographic trends), and the productivity growth rate in our model to estimate u-optimal. Traditional methods utilize a fixed coefficients approach to estimate the natural rate. That is, an analyst would pick a sample period (for example, Ball and Mankiw utilized the sample period) to estimate the model and utilize those estimated coefficients to generate the natural rate. However, a fixed coefficients approach assumes the nature of the risk is constant for the complete period. Since economies evolve over time and risks to the economic outlook constantly change, an Phillips, A.W. (198). The Relation between Unemployment and the Rate of Change of Money Wage rates in the United Kingdom Economica Vol 2, No 10. Ball, Laurence and N. Gregory Mankiw. (2002) Ibid. Staiger, D. James Stock and Mark Watson. (1997). How Precise are Estimates of the Natural Rate of Unemployment? in Reducing Inflation: Motivation and Strategy by Romer, C and Romer D. University of Chicago Press. 2

3 evolving set of coefficients is necessary when estimating the natural rate, or u-optimal. For example, the nature of inflation risk to the economic outlook has changed significantly during the past four decades or so. That is, double-digit inflation rates (higher inflation or inflationary pressure) were last seen in the early 1980s, while inflation rates have averaged close to 2% during most of the post-1990 era. Similarly, the last three recoveries have been labeled as jobless, making them very different from the pre-1990 era s recoveries. Naturally, a time-varying set of coefficients is more effective in addressing the contemporary risks and is needed to estimate the u-optimal rate for different periods. The Inflation/Growth Outlook Probabilities as Key Inputs of the Model Our past work developed an ordered Probit model to forecast the probability of inflationary pressure, deflationary pressure and price stability. We characterize the inflation series (PCE deflator growth rates), into inflationary pressure (PCE deflator above 2.%), deflationary pressure (PCE deflator below 1.%) and stable prices (PCE deflator between 1.% and 2.%). We predict two-quarters ahead probabilities of each inflation outlook. The inflation outlook probabilities are plotted in Figure 1. The bars (shaded area) above zero represent actual periods of inflationary prices, or periods of PCE deflator growth rates greater than 2.%. Similarly, the bars below the zero line indicate periods of deflationary pressure, or periods during which the PCE deflator growth rates were below 1.%. The unshaded areas (between 199 and 1997, for example) show periods during which prices were stable (PCE deflator growth rates between 1.% and 2.%). Our model has predicted all inflation outlook episodes accurately, in a stimulated real-time analysis, making it a reliable measure to estimate near-term inflation expectations. Figure 1 Figure The -Month Ahead Probability of Inflation Scenarios Probability of Deflationary Pressure (PCE < 1.%) - Probability of Stable Prices (1.% PCE 2.%) Probability of Inflationary Pressure (PCE > 2.%) Two-Quarter Ahead Probability of Growth Scenarios Probability of a Strong Recovery Probability of a Weak Recovery Probability of a Recession We utilize Probit models to predict probabilities of the inflation and growth outlook. Source: Wells Fargo Securities In a 201 report, we presented a framework that characterized growth in three categories: recessions, weaker recoveries and stronger recoveries. 7 We developed an ordered Probit model to predict two-quarter ahead probabilities of these three growth scenarios. The probabilities are depicted in Figure 2. The model predicted all episodes of the three growth scenarios in a simulated real-time analysis and therefore we can utilize these probabilities to capture the near-term growth outlook in our model. We utilize these two Probit models to predict probabilities of the inflation and growth outlook to be utilized as key determinants of our u-optimal model. Predicting the Probability of Inflation/Deflation: An Ordered Probit Approach. (February 17, 201) Available upon request. 7 Predicting the Probability of Recession and Strength of Recovery: An Ordered Probit Approach. (July 19, 201).

4 Our proposed method, the u-optimal rate, is better than some traditional options. Estimating the U-Optimal Rate Our approach includes probabilities of the inflation and growth outlooks, as well as the labor force participation rate and the productivity growth rate, as key determinants of u-optimal. We utilize two different benchmarks to show the effectiveness of our approach. The first benchmark is the Congressional Budget Office (CBO) measure of the natural unemployment rate. 8 The second benchmark is a purely statistical method known as the Hodrick-Prescott (H-P) filter. The H-P filter estimates a long-run trend for the unemployment rate, which can be interpreted as the natural unemployment rate. We use data through Q-2018 to compute the natural unemployment rate based on several different methods. The results, as well as standard errors of the regressions, are reported in Table 1. 9 We also added a column disclosing the difference between the upper and lower values of the range, which is labeled as gap. A wider gap would reduce the effectiveness of the natural rate for policymakers, as suggested by Staiger, Stock and Watson (1997). The Phillips Curve method which is a fixed-coefficient approach produced the largest gap (2.8%) followed by the H-P filter (2.%). Our method and the CBO estimates have produced the same gap of %. The smallest gap (0.9%) was produced by the four quarter-moving-average (-QMA) of the u-optimal. Utilizing the gap as a gauge of the precision of an estimate of the natural unemployment rate, our proposed method, is better than some traditional options. In addition to the upper/lower limits and gap, the level of the estimated u-optimal is also important. While the u-optimal rate and the CBO estimates have the same gap, the economic/inflation outlook and monetary policy assumptions may be different based on these two different methods. The actual unemployment rate for Q-2018 was.8%, which is lower than the CBO s natural rate estimate of.% and our estimate of u-optimal of.1%. The actual unemployment rate is also below (outside of) the estimated range of the CBO, which is.1% to.1%. An implication of the CBO s estimated range of the natural unemployment rate is that the FOMC may need to tighten policy at a faster rate in order to head off inflationary pressures. Table 1 Figure Method* Estimate Upper- Limit Lower- Limit The H-P Filter (N/A).0%.% 2.7% Gap** 2.% Unemployment Rate Actual, U-Optimal, CBO's NAIRU Unemployment Rate: U-Optimal: CBO Natural Rate: Traditional Method, Phillips Curve (1.0%).7%.1%.% 2.8% U-Optimal (0.7%).1%.%.% % 7 7 -QMA of U-Optimal (N/A).2%.%.7% 0.9% CBO Estimate (N/A).%.1%.1% *Standard errors of the regression are in parantheses ** Difference between the upper and lower values of the range % Source: U.S. Department of Labor, Congressional Budget Office and Wells Fargo Securities The actual unemployment rate, however, falls within the range (.% to.%) of our u-optimal methodology. Our estimated range suggests that Fed policymakers should continue to remove policy accommodation, but that they should do so at a gradual pace because the actual 8 For additional detail, see the CBO website. 9 We reported standard errors only for the Phillips curve and modified Phillis curve methods because we have estimated those equations and thereby have standard errors for those methods. The H-P filter is a trend-fitting-based method and the CBO does not report standard errors for the NAIRU calculations. Further, we utilize standard deviations of these methods to draw upper and lower limits. The upper and lower limits of the Phillips curve and modified Phillips curve are based on the standard errors of those equations.

5 unemployment rate is still above the lower limit of our estimated range. For effective policymaking, both the level of the natural rate and the gap (as upper/lower limit) are important. An additional point to stress, which would assist policymakers, is that the estimated natural unemployment rate should be consistent with the phases of the business cycle. During recessions and early phases of recoveries, it would be helpful for the FOMC to gauge slack in the labor market (how far above the natural rate the actual unemployment rate is) and overheating during expansions (how far below the natural rate the actual unemployment rate is). In the former scenario, the FOMC would evaluate the amount/duration of the accommodative monetary policy stance, while the latter would help the FOMC to identify the timing/magnitude of policy normalization. We acknowledge the secular decline of the natural unemployment rate over the past few decades. The CBO s estimate of natural unemployment rate remained constant in the second half of the 1970s but then trended lower up to the Great Recession (Figure ), and there have been four recessions in that period. The natural rate should rise somewhat during recessions and then recede during expansions, but the CBO s natural rate only acknowledged that dynamic for the post Q period (only due to the Great Recession). A natural unemployment rate that fails to rise during a recession may result in overly accommodative monetary policy during the subsequent recovery. Policymakers may think that labor market slack is larger than the true slack in the economy (which would be based on the rising natural rate). Our estimate of the u-optimal accounts for the business cycles (Figure ). That is, both the actual unemployment rate and our estimated u-optimal move up during a recession, but the unemployment rate tends to move faster (higher than the u-optimal rate). Moreover, the u-optimal follows a downward trend for the pre-great Recession era, which is consistent with the CBO s estimate of the natural unemployment rate over the same period. A Statistical Rationale for Regime-Switching U-Optimal We conduct a statistical analysis to support the utilization of a time-varying (different coefficients for different periods) approach, rather than relying on a fixed-weight method. We employ the period for the statistical analysis, and the results are reported in Table 2. We utilize four different sub-samples to test the statistical robustness of the results, and divide the dataset into sub-samples to represent different growth/inflation/interest rate regimes. For example, the period contains relatively higher growth, inflation and interest rates, on average, compared to the other sub-samples. The post-1990 era experienced moderate growth/inflation/interest rates, compared to the pre-1990 period. The post-2000 period experienced relatively lower growth and inflation/interest rates compared to the pre-2000 era. 10 Naturally, a different level of u-optimal is expected in those different periods. It is also possible that the strength of the relation between the unemployment rate and its drivers is different during these sub-samples. The root mean squared error (RMSE), which is a measure of a model s fit, is also exhibited in Table 2. Smaller values of RMSE imply better model accuracy. The sample period has the largest RMSE, which indicates a relatively poor fit. Different RMSEs for different sub-samples support the view that a time-varying coefficient approach is appropriate. The average u-optimal is different for different sub-samples as well as for the complete period. Since different samples have different RMSEs and u-optimals, for a fair comparison, we calculate the ratio of the RMSE to u-optimal. For example, the sub-sample has the largest RMSE but this period has the highest average u-optimal. In considering both the RMSE and average u-optimal, this ratio allows us to compare different samples fairly. The complete period ( ) still shows the highest uncertainty as it has the largest ratio. If we utilize the complete period s RMSE to construct the The estimated natural unemployment rate should be consistent with the phases of the business cycle. 10 The other possible choice to divide the dataset into sub-samples is the data division according to business cycles. However, lengths of business cycles vary significantly from a range of 12 ( business cycle) to 120 months ( business cycle). Furthermore, some business cycles shorter time span may affect the statistical accuracy of our results. Therefore, we divide data into sub-samples to represent different economic regimes and to avoid shorter time span.

6 upper and lower limits of the u-optimal, it would be the widest interval. That strongly suggests that we should not use the fixed-coefficient approach to estimate the u-optimal. Table 2 Our u-optimal estimate could help the Fed in its implementation of monetary policy. Sample Period RMSE* U-Optimal Ratio of RMSE to U-Optimal* *A higher value indicates higher uncertainty/ Source: Wells Fargo Securities Concluding Remarks: Where There s a Will, There s a Way This report presents a new approach to estimate the natural rate of unemployment. We believe our framework, which relies on time-varying methods while accounting for impending risks, accurately estimates the natural unemployment rate. Our u-optimal estimate could help the Fed in its implementation of monetary policy. Therefore, we will discuss the implications of our u-optimal methodology for Fed policy in a follow-up non-technical report.

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