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Minimizing Recessionary Impacts and Share Risk with Quasi-Real Minimizing Recessionary Impacts and Share Risk With Quasi-Real Indexing and Nominal GDP Targeting By David Eagle Associate Professor of Finance Eastern Washington University Email: [email protected] Phone: (509) 828-1228 Abstract: The Pareto-optimal goal for monetary and fiscal policy should be to minimize “share risk,” the risk that a predetermined future payment as a share of the economy will differ from expectations. Deviations of this share from expectations is inversely related to NGAP, the deviation of nominal GDP (NGDP) from its expectations. Most of the unemployment during and following USA recessions is explained by current and lagged NGAPs, and simulations show successful NGDP targeting eliminates over 75% of the longer-term unemployment associated with recessions. Given that aggregate employment compensation is a constant share of NGDP, a negative NGAP necessarily leads to employment declining when wages are fixed. For employment to be unaffected by NGAP, the average wage rate must be a constant share of NGDP. While the appropriate target to minimize share risk should be NGDP, contracts themselves can minimize share risk through quasi-real indexing. JEL codes: E52, E24 Keywords: nominal GDP targeting, inflation targeting, unemployment, business cycle October 14, 2013 © Copyright 2013, by David Eagle. All rights reserved. Minimizing Recessionary Impacts and Share Risk With Quasi-Real Indexing and Nominal GDP Targeting I. Introduction An almost consensus exists among the world’s central banks that one of their primary goals, if not their primary goal, should be price stability, which is often interpreted as minimizing inflation risk. Rather than accepting this “consensus” goal of price stability or of minimizing inflation risk, this paper applies the Pareto criterion to a pure-exchange economy of diverse consumers. We find that instead of minimizing inflation risk, instead of minimizing price-level risk, central banks should try to minimize what we call “share risk.” Share risk is the risk that a predetermined future payment as a share of the economy will differ from initial expectations. Our concept of share risk should not be confused with the microeconomic share in Weisman’s (1984) “The Share Economy.” Weisman’s proposal was to have wages set as shares of the individual employers’ profits; hence, we refer to Weisman’s share as a microeconomic share. In this paper, we talk about wages and other predetermined future payments as shares of the whole economy; hence, we view our share concept as a macroeconomic share. The issue at hand is the role of money as a unit of account for future contractual payments. For a particular future contractual payment, define its share to be that payment divided by nominal GDP (NGDP). We argue that the optimal unit of account is one that minimizes the deviation of this share from what the contractual parties expected that share to be when they agreed to the contract. As section III shows, when real GDP remains the same, the justification economists usually give to minimize inflation risk rigorously should be to minimize price-level risk, not - 1 - inflation risk. However, when we allow real GDP to change in a pure-exchange economy, Koenig (2013), Eagle and Christensen (2012), and Eagle and Domian (2005) show, the Pareto- efficient consumption for individuals with average relative risk aversion should be a constant share of the economy. For their consumption to be a constant share of the economy, predetermined future payments usually need to be a constant share of the economy as well. The issue of share risk extends beyond pure-exchange economies. Using USA data, we find that aggregate wages and salaries as a share of NGDP remains relatively constant over the duration of a recession. Given this constancy, fixed wages will necessarily lead to below- expected employment levels when NGDP is below initial expectations. A necessary and sufficient condition for employment to be unaffected by unexpected changes in NGDP is for the average wage rate to be a constant share of the economy rather than a fixed nominal amount. Setting wage rates as a fixed share of the economy is exactly what quasi-real indexing does (See, Eagle and Domian, 1995, 2005). Quasi-real indexing, by construction, keeps predetermined wage rates and other future prices as constant shares of the economy. However, for quasi-real indexing to work well, all contracts must be quasi-real indexed. Otherwise, declines in NGDP will cause some agents to be squeezed between declining quasi-real-indexed income and fixed nominal expenses. Given the difficulties in converting all contracts to quasi-real indexing and given the difficulty in changing the public’s mindset to accept universal quasi-real indexing, the best way to minimize share risk is for the central bank to target NGDP, which should minimize the deviation of actual NGDP from expected NGDP, which by definition will minimize share risk. This paper goes beyond theory and empirically studies the relationship between NGAP and unemployment around recessions using paneled USA data. NGAP is defined as the - 2 - Figure 1. Excess Unemployment Rate (ExUR) and USA Recessions 4.00% 3.00% 2.00% 1.00% average 0.00% -4 -1.00% 0 4 8 12 16 19491948 Recession -2.00% quarters after recession beginning deviation of NGDP from its expected level, which we operationally define as the prerecession trend of NGDP. Figures 1 and 2 show the motivation for our empirical research. In Figure 1, the variable ExUR represents the excess of the unemployment rate over the prerecession unemployment rate. On average, the unemployment rate in the USA has taken well over four years (16 quarters) to return to its prerecession level. However, the USA’s Recession of 1949 is an exception, where the unemployment rate returned to its prerecession rate in about two years. Figure 2 provides an answer to the question of what made the USA’s Recession of 1949 different. NGAP, which at the beginning of the recession spiked downward, returned to zero within two years of the recession’s beginning, preceding the return of unemployment to its prerecession level by about two quarters. The USA’s experience during the Recession of 1949 Figure 2. USA Recession of 1949 - Relationship Between Excess Unempl. Rate and NGAP 6.00% 4.00% %NGAP 2.00% Ex Un 0.00% Rate -2.00%Jan-48 Jan-49 Jan-50 Jan-51 Jan-52 Jan-53 -4.00% -6.00% -8.00% -10.00% - 3 - has inspired this paper’s investigation into the degree to which NGAP explains unemployment. Figure 3 shows how closely our model’s estimate of unemployment compares to actual unemployment. We find that a regression of unemployment against current and lagged NGAP results in an R2 of over 70%. Section II of this paper discusses in more detail our empirical investigation into the relationship between NGAP and unemployment and our empirically-based simulations into how NGDP targeting can reduce over 75% of the longer-term unemployment following a recession. Section III discusses the theoretical basis for the goal of minimizing share risk in the context of a pure-exchange economy. Section IV extends the concept of share risk to economies with labor markets. Section V discusses quasi-real indexing and relates this type of indexing to the wage indexation literature. Section VI summarizes, concludes, and reflects upon this papers’ findings, not only for monetary policy, but for fiscal policy as well. II. Empirical Relationship between Unemployment and NGAP This section reports on our empirical analysis into the relationship between unemployment and NGAP. In order to Figure 3: Average Predicted vs. Actual ExUR for determine NGAP, we first need to the six U.S. recessions, not including the 1969 and 1973 recessions. determine the prerecession trend for NGDP, which can be expressed as 4t Nt N0 (1 k) where time 0 is the official beginning of the recession, k is the annual trend growth rate, and time is measured in quarters. Quarter t is t quarters since recession beginning - 4 - quarters after the beginning quarter, and quarter –t means t quarters before the beginning quarter (e.g., quarter -4 is the quarter 4 quarters before the beginning quarter). Taking the natural logarithm of both sides gives a linear relationship: ln(Nt ) ln(N0 ) ln(1 k) 4t . To determine the prerecession trend, we regressed ln(Nt ) on ln(N 0 ) and the negative values of t that represented the quarters in the prerecession time period identified in Table A-1 in Appendix A. ˆ Where the resulting linear estimate is ln(N t ) aˆ bt , the trend’s estimate for NGDP at time 0 is e aˆ and the estimate for the trend’s annual growth rate for NGDP is ebˆ / 4 1 . Because our focus is on NGAP, our determination of quarter 0 for some recessions differs from the official beginning of some recessions. For the Recession of 1949 and the 1973- 1975 Recession, the significant negative NGAPs showed up the quarter following the official recession beginning; therefore, we designated that following quarter as quarter 0. For the early 2000s recession, NGAP became negative two quarters prior to the official beginning of the recession. For the Great Recession (2007-2008), NGAP first became significantly negative three quarters after the official beginning of the recession. For details, see Table A-1 in the Appendix. We also considered there to be two sets of “double-dip” recessions: (i) the Recession of 1958 and of 1960-61, and (ii) the 1980 and Early 1980s recessions. For the second dip of each of these “double-dip” recessions, we based NGAP on the NGDP trend established prior to the first dip. Hence the “quarter 0” designation for the second dip has no consequence.
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