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Authorized for public release by the FOMC Secretariat on 1/12/2024 January 2018 Metro Level Evidence on the Convexity of the U.S. Phillips Curve Anthony Murphy, Federal Reserve Bank of Dallas 1 1. Introduction and Summary of Findings Is the U.S. Phillips Curve convex? Does upward pressure on inflation rise increasingly as unemployment falls below the natural rate of unemployment? If so, should monetary policy makers act pre-emptively and raise interest rates sooner rather than later? The evidence for the convexity of the Phillips Curve is rather mixed. Most studies find a convex wage inflation Phillips Curve, but few studies find a convex price inflation Phillips Curve My research using metro level inflation and unemployment data suggests that the price Phillips Curve is “alive”, since labor market slack is always economically and statistically significant. Although the fit of convex Phillips Curves is sometimest better than the fit of linear curves, the degree of convexity in the Phillips curve is modest, and is not economically significant. 2. Review of the Existing Evidence The evidence for the convexity of the U.S. Phillips Curve is rather mixed. Most studies find a convex wage inflation Phillips Curve, but few studies find a convex price inflation Phillips Curve (Tables 1 and 2). From a policy viewpoint, convexity of the price Phillips Curve is more important since the pass through from wage inflation to price inflation is not that strong. For example, Peneva and Rudd (2015) “find little evidence that changes in labor costs have had a material effect on price inflation in recent years, even for compensation measures where some degree of pass through to prices still appears to be present”. Many researchers argue that aggregate data may not be sufficiently informative about the convexity of the wage and price Phillips Curves, especially when the Fed successfully Email: anthony.murphy@dal.frb.org. The view expressed in the paper are my own, and not those of the Federal Reserve Bank of Dallas or the Federal Reserve System. 1 1 Authorized for public release by the FOMC Secretariat on 1/12/2024 targeted inflation during the Great Moderation period. They suggest that U.S. regional or metro data may be more informative, and many recent papers adopt this approach. Two recent papers, which have been cited by Chair Yellen, convey a flavor of the recent findings. Kumar and Orrenius (2016) use state level data to detect convexity in the wage Phillips Curve. They find “strong evidence that the wage-price Phillips curve is nonlinear and convex; declines in the unemployment rate below the average unemployment rate exert significantly higher wage pressure than changes in the unemployment rate above the historical average.”. The estimated wage Phillips curve is twice as steep when the unemployment rate is low than when it is high. This means that the upward pressure on wages from a fall in the unemployment rate is twice as large when the rate is low than when it is high. Nalewaik (2016) uses long time series of aggregate data from the 1960s and a model with different inflation regimes to jointly model U.S. wage and price inflation. In contrast to Kumar and Orrenius (2016), he finds a relatively linear wage Phillips Curve, and a convex price inflation Phillips Curve. He reports finding “a sharp steepening of the (price) Phillips curve after labor market slack becomes sufficiently negative, so the effect of slack on inflation becomes much larger after labor markets tighten beyond a certain point.” 3. Metro Level Data Since it is difficult to identify convexity in the Phillips Curve using aggregate data covering the Great Moderation period, I exploit the greater time series and cross section variation in inflation and unemployment rates at the metro level. I use semi-annual core CPI inflation (𝜋𝜋 𝑐𝑐 ) and unemployment (𝑢𝑢) data from the mid-1980’s for a panel of 27 large U.S. metros. I also use quarterly data for about half of these metros. Inflation is measured as the deviation of the metro level, year-on-year core CPI inflation rate from the long-term (10-year) expected inflation rate in the Survey of Professional Forecasters (𝜋𝜋𝑚𝑚 − 𝜋𝜋� 𝑒𝑒 ). Labor market slack is measured as the difference between the metro unemployment rate and the CBO’s estimate of the natural rate of unemployment or NAIRU for the U.S. (𝑢𝑢𝑚𝑚 − 𝑢𝑢𝑁𝑁𝑁𝑁𝑁𝑁 ). 2 Authorized for public release by the FOMC Secretariat on 1/12/2024 4. Models and Results Inflation depends on expected long term inflation ( π e ), past inflation and lagged measures of labor market slack and lagged changes in slack. I estimate a variety of Phillips Curves with linear, linear spline and convex slack effects since theory does not specify the functional form of the Phillips Curve when it is convex. In the spline specifications, the two terms are um − u NRU and min(0, um − u NRU ) . In the non-linear specifications, convexity may be captured by using ln(um / u NRU ) or ugapm / u as the slack terms. Inter alia, I estimate a broader class of models, use higher frequency data and take account of more factors than other researchers do. For example, heterogeneous dynamic panel data models with multiple unobserved common factors are estimated. Some semi-annual estimation results are presented and discussed in the Appendix. First, I find that the price Phillips Curve is still “alive”, in the sense that labor market slack is always economically and statistically significant. In addition, there is no compelling evidence of a significant decline in the effect of slack on inflation in the metro-level dataset. Second, the fit of convex Phillips Curves is sometimes better than the fit of linear Phillips Curves. Third, despite this, the degree of convexity in the Phillips curve is modest, and is not economically significant. 5. Does Convexity Matter Two related ways – one informal, the other more formal - of assessing the importance of the convexity of the Phillips Curve are considered. First, I check whether the estimated linear and convex Phillips Curves are very far apart when slack is negative (the unemployment rate is below the NAIRU)? The answer is no – the estimated linear and convex Phillips Curves are close when slack is negative in the historically relevant range, i.e. - 0% to -2% in the metro panel, and 0% to -1% at the aggregate level. Three different estimated Phillips Curves are plotted in Figure 1 – a linear curve (the red line) and two convex curves (the blue and green lines). The unemployment gap is measured on the horizontal axis and the deviation of inflation from long 3 Authorized for public release by the FOMC Secretariat on 1/12/2024 term expected inflation on the vertical axis. When unemployment is low, the unemployment gap is negative and inflation is high. The rise in inflation is greater the more convex the Phillips Curve. Generally, when unemployment is relatively low, we observe (negative) slack values between 0 and -1%. Within this range, the differences in the inflation rates associated with the linear and convex Phillips Curves is very small, so the effect of convexity is not economically significant. Second, I check whether the results of simulating an exogenous fall in slack in a simple, three equation IS-PC-MR model differ significantly when the Phillips Curve is linear vs. when it is convex? The dynamics of the IS curve are based on estimates from before the Great Recession. The two Phillips curve are based on the quarterly linear and convex (slack = 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 / 𝑢𝑢𝑚𝑚,𝑡𝑡 ) DCCE estimates. An inertial Taylor Rule is used, with inertia coefficient of 0.85 and equal weights on the deviation of inflation from target and the unemployment gap. The NAIRU and inflation target are assumed to fixed, and inflation expectations are either constant or slowly adjusting. The results of simulating the effects of a temporary decline in the unemployment rate suggest that the degree of convexity in the Phillips Curve is modest (Figure 2). IIn the simulations, a short-term shock that reduces the unemployment rate by one percentage point boosts core CPI inflation by 30 basis points (bps) when the Phillips Curve is linear, and less than 40 bps when it is convex. If inflation expectations adjust modestly, the effects might be 15 bps higher. Similar results hold in more elaborate models. Conclusion The degree of convexity in the price Phillips Curve appears to be relatively small, and not economically significant. Labor market slack is always economically and statistically significant. Although the fit of convex Phillips Curves is sometimes better than the fit of linear curves, the degree of convexity is modest. References Albuquerque, B., Baumann, U. (2017), “Will U.S. inflation awake from the dead? The role of slack and non-linearities in the Phillips Curve, European Central Bank working paper no. 2001. 4 Authorized for public release by the FOMC Secretariat on 1/12/2024 Ball, L., Mazumder, S. (2011), “Inflation dynamics and the Great Recession”, Brookings Papers on Economic Activity, 42(1), 337-405. Chudik, A., Pesaran, M. H. (2015), “Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors”, Journal of Econometrics, 188 393-420. Daly, M., Hobijn, B. (2014), “Downward nominal wage rigidities bend the Phillips Curve”, Journal of Money, Credit, and Banking, 46, 51-93. Detmeister, A., Babb, N. (2017), “Nonlinearities in the Phillips Curve for the United States”, mimeo. Donayre, L., Panovska, I. (2016), “Nonlinearities in the U.S. wage Phillips Curve”, Journal of Macroeconomics, 48, 19-43. Fallick, B., Lettau, M., Wascher, W. (2016), “Downward nominal wage rigidity in the United States during and after the Great Recession”, Finance and Economics Discussion Series 2016-011, Washington: Board of Governors of the Federal Reserve System. Fisher, R., Koenig, E. (2014), “Are we there yet? Assessing progress towards full employment and price stability”, Federal Reserve Bank of Dallas Economic Letter, (9)13, 1-4. Kumar, A., Orrenius, P. (2016), “A closer look at the Phillips curve using state-level data”, Journal of Macroeconomics, 47(A), 84-102. Laxton, D., Rose, D., Tambakis, D. (1998), “The U.S. Phillips curve: the case for asymmetry”, Journal of Economic Dynamics & Control, 23, 1459-85. Murphy, A. (2017), “Is the U.S. Phillips Curve Convex? Some Metro Level Evidence”, mimeo. Nalewaik, J. (2016), “Non-linear Phillips curves with inflation regime switching”, Finance and Economics Discussion Series 2016-078, Board of Governors of the Federal Reserve System. Peneva, E., Rudd, J. (2015), “The passthrough of labor costs to price inflation,” Finance and Economics Discussion Series 2015-042. Washington: Board of Governors of the Federal Reserve System. Yellen, J. (2015), “Inflation Dynamics and Monetary Policy”, Philip Gamble Memorial Lecture, University of Massachusetts, Amherst, September 24. 5 Authorized for public release by the FOMC Secretariat on 1/12/2024 Table 1: Recent Studies of the Wage Phillips Curve in the U.S Study Data Main Model Finding Daly & Hobijn (2014) CPS y/y wage growth data, 1986 to 2012 No model Suggestive - Nominal downward rigidities increase in recessions; convex PC Fisher & Koenig (2014) Quarterly ECI wage & salary growth, 1984 Q1 to 2014 Q2 Linear model with lagged level and inverse of unemployment rate Strong - convex PC Donayre & Panovska (2016) Quarterly aggregate data; earnings of production & non-supervisory workers; 1965-1984 Three regime threshold regression model depending on unemployment rate Strong - convex PC with significantly different regime dynamics Kumar & Orrenius (2016) Annual state level CPS ORG average hourly wage, 1982 to 2013 Fixed effects panel model with linear unemployment spline Strong - convex PC Nalewaik (2016) Annual data, core PCE inflation and growth in non-farm business sector hourly compensation, 1961 to 2015 Two equation, two regime Markov Switching model with squared low unemployment rate term; one regime is nonstationary Weak - limited convexity in wage PC; Notes: ECI = employment cost index, PC = Phillips Curve and y/y = year-over year. Additional evidence of downward nominal ECI wage rigidity is provided by Fallick, Lettau and Wascher (2016). 6 Authorized for public release by the FOMC Secretariat on 1/12/2024 Table 2: Recent Studies of the Price Phillips Curve in the U.S. Study Data and Sample Main Model Finding Laxton, Rose & Tambakis (1999) Quarterly CPI inflation, 1968 Q1 to 1997 Q1 Two equation model; PC with time varying coefficient on convex unemployment gap term and random walk NRU Weak - convex PC, but fit only marginally better than for linear model Ball & Mazumder (2011) Quarterly data, y/y headline and core (median) CPI, 1960q1 Linear model where slope of PC varies with level and/or variance of inflation Mixed - prefer model with varying slope to convex PC model; fit of linear and convex PC models similar Nalewaik (2016) Annual data, core PCE inflation and growth in non-farm business sector hourly compensation, 1961 to 2015 Two equation, two regime Markov Switching model with squared low unemployment rate term; one regime is nonstationary Strong - convex PC Albuquerque & Baumann (2017) Quarterly data, y/y PCE inflation, 1992 Q1 – 2015 Q1 Time varying parameter model using unemployment gap and labor market tracking index etc. Weak - prefer time varying parameter to convex PC model; fit of linear and convex PC models similar. Detmeister & Babb (2017) Annual metro data, core CPI inflation, 1984 to 2016 Fixed effects panel model Weak - some convexity but not economically significant Murphy (2017) Sem-annual and quarterly metro data, core CPI inflation, 1984 to 2016 Fixed effects and dynamic correlated common effects panel models. Weak - some convexity but not economically significant Notes: See Table 1. 7 Authorized for public release by the FOMC Secretariat on 1/12/2024 Figure 1: Is the Convexity of the Phillips Curve Important? Source: Murphy (2017) 8 Authorized for public release by the FOMC Secretariat on 1/12/2024 Figure 2: Simulated Effects of a Temporary Fall in the Unemployment Rate (a) Time Path of the Unemployment Rate (b) Time Path of Inflation – Linear (Blue Line) and Convex (Red Line) Phillips Curves Note: Long-term inflation expectations are anchored at 2.3%. Source: Murphy (2017). 9 Authorized for public release by the FOMC Secretariat on 1/12/2024 Appendix: Some Econometric Results Data and Models The effect of labor market slack on inflation are identified using the using time series and cross-section variation in unemployment and core CPI inflation rates at the metro level. The models are formulated in term of the deviations of inflation from survey based, long run expected inflation and the deviation of the unemployment rate from the NAIRU. • • • 𝑐𝑐 𝑐𝑐 𝜋𝜋�𝑚𝑚,𝑡𝑡 = 𝜋𝜋𝑚𝑚,𝑡𝑡 − 𝜋𝜋�𝑡𝑡𝑒𝑒 = Devistion of core year-on-year CPI inflation in metro m from longterm expected inflation in the Survey of Professional Forecasters (SPF). 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 = 𝑢𝑢𝑚𝑚,𝑡𝑡 − 𝑢𝑢𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁 = Unemployment gap, the deviation from the CBO’s natural rate of unemployment or NAIRU. 𝑛𝑛𝑛𝑛𝑛𝑛 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 = 𝑚𝑚𝑚𝑚𝑚𝑚�0, 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 � = Negative unemployment gap (i.e. tight labor market). Models with linear, linear spline and convex labor market slack effects estimate. The base linear spline model is: 𝑛𝑛𝑛𝑛𝑛𝑛 𝑐𝑐 𝑐𝑐 𝑐𝑐 𝜋𝜋�𝑚𝑚,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1 𝜋𝜋�𝑚𝑚,𝑡𝑡−1 + 𝛽𝛽2 𝜋𝜋�𝑚𝑚,𝑡𝑡−2 + 𝛽𝛽3 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 + 𝛽𝛽4 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 + 𝛽𝛽5 ∆𝑢𝑢𝑚𝑚,𝑡𝑡−2 + 𝑣𝑣𝑚𝑚,𝑡𝑡 where: 𝑐𝑐 𝑐𝑐 𝜋𝜋�𝑚𝑚,𝑡𝑡 = 𝜋𝜋𝑚𝑚,𝑡𝑡 − 𝜋𝜋�𝑡𝑡𝑒𝑒 = Devistion of core year-on-year CPI inflation in metro m from long-term expected inflation in the Survey of Professional Forecasters (SPF). 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 = 𝑢𝑢𝑚𝑚,𝑡𝑡 − 𝑢𝑢𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁 = Unemployment gap, the deviation from the CBO’s natural rate of unemployment or NAIRU. 𝑛𝑛𝑛𝑛𝑛𝑛 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 = 𝑚𝑚𝑚𝑚𝑚𝑚�0, 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 � = Negative unemployment gap (i.e. tight labor market). The model is an expectations augmented Phillips Curve, as opposed to a New Keynesian Phillips 𝑛𝑛𝑛𝑛𝑛𝑛 Curve, with priors: 𝛽𝛽3 < 0, 𝛽𝛽4 < 0 �𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 < 0� 𝑎𝑎𝑎𝑎𝑎𝑎 𝛽𝛽5 < 0. The data are I(0), and the choice of lags is based on limited pre-searching. Other convex specifications for the effect 𝑛𝑛𝑛𝑛𝑛𝑛 of slack use 𝑢𝑢𝑔𝑔𝑎𝑎𝑎𝑎𝑚𝑚,𝑡𝑡 and 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 squared as in Nalewaik (2016), 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡 / 𝑢𝑢𝑚𝑚,𝑡𝑡 as in Debelle and Vickery (1998), or log slack, 𝑙𝑙𝑙𝑙(𝑢𝑢𝑚𝑚,𝑡𝑡 /𝑢𝑢𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁 ). The Phillips Curves are estimated using pooled OLS, one and two-way fixed effects and dynamic common correlated effects (DCCE) estimators. The DCCE estimator (Chudik and Pesaran, 2015) is the most general one and has many advantages: 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 𝜋𝜋�𝑚𝑚,𝑡𝑡 = 𝛽𝛽𝑚𝑚,0 + 𝛽𝛽𝑚𝑚,1 𝜋𝜋�𝑚𝑚,𝑡𝑡−1 + 𝛽𝛽𝑚𝑚,2 𝜋𝜋�𝑚𝑚,𝑡𝑡 + 𝛽𝛽𝑚𝑚,3 (𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 /𝑢𝑢𝑚𝑚,𝑡𝑡−2 ) + ∑𝑗𝑗 𝛾𝛾𝑚𝑚,𝑗𝑗 𝑓𝑓𝑗𝑗,𝑡𝑡 +𝑣𝑣𝑚𝑚,𝑡𝑡 10 Authorized for public release by the FOMC Secretariat on 1/12/2024 It provides consistent estimates of the mean effects in dynamic, heterogeneous panel data models with weakly exogenous variables and cross section dependence. The cross section dependence is modelled in a flexible way (as unobserved factors 𝑓𝑓𝑗𝑗,𝑡𝑡 ), which are “partialed out” by adding current and lagged cross section averages of the dependent regressors and other related covariates to the individual equations. Some representative regression results are set out in Table A. Consider the linear spline results initially. The pooled OLS and FE results are very similar - inflation is highly persistent; lagged labor market slack and changes in slack are economically and statistically significant. The linear spline term in lagged slack is significant suggesting that the Phillips Curve is convex. However, the pooled OLS and FE results do not account of any common omitted factors, such as imported core goods inflation, driving metro-level inflation. The DCCE results, which do, are rather different. Inflation is not as persistent and lagged labor market slack, but not the lagged change in slack, is significant. The spline term is insignificant, which suggests that the Phillips Curve is linear. Other convex specifications need to be examined before reaching this conclusion. The fit of the two convex models is about the same as that of the linear / linear spline models. Similar results are obtained using quarterly data for approx. 13 metros and in subsamples. Lagged labor market slack is always economically and statistically significant. The linear spline term is also insignificant in the DCCE results. Convex Phillips Curve models fit marginally better. The effects of slack are fairly stable in the sub-samples. Changes in lagged slack are also statistically significant in the quarterly models, but are hard to identify in the sub-samples. Results hold up to various robustness checks – breaks in CPS-based unemployment series, threshold effects, alternative measures of expected inflation etc. 11 Authorized for public release by the FOMC Secretariat on 1/12/2024 Table A: Linear Spline and Convex Phillips Curve Specifications 𝑐𝑐 𝑐𝑐 Dependent Variable: 𝜋𝜋�𝑚𝑚,𝑡𝑡 = 𝜋𝜋𝑚𝑚,𝑡𝑡 − 𝜋𝜋�𝑡𝑡 . Sample: 24 to 27 Metros, 1985 or 1986 H1 to 2016 H2 (Semi-Annual). Regressors 𝑐𝑐 𝜋𝜋�𝑚𝑚,𝑡𝑡−1 𝑐𝑐 𝜋𝜋�𝑚𝑚,𝑡𝑡−2 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 𝑁𝑁𝑁𝑁𝑁𝑁 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 ∆𝑢𝑢𝑚𝑚,𝑡𝑡−2 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚,𝑡𝑡−2 /𝑢𝑢𝑚𝑚,𝑡𝑡−2 𝑁𝑁𝑁𝑁𝑁𝑁 ln�𝑢𝑢𝑚𝑚,𝑡𝑡−2 ⁄𝑢𝑢𝑡𝑡−2 � ∆ ln 𝑢𝑢𝑚𝑚,𝑡𝑡−2 Metro Fixed effects Adjusted R2 SE No of Observations Linear Spline in 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚 OLS FE DCCE 0.867*** 0.836*** 0.670*** (0.027) (0.025) (0.032) -0.244*** -0.256*** -0.331*** (0.023) (0.022) (0.030) -0.017 -0.032** -0.319*** (0.012) (0.012) (0.053) -0.195*** -0.235*** (0.036) (0.039) -0.172*** -0.163*** (0.029) (0.021) 0.621 0.671 1679 Yes 0.609 0.661 1679 0.620 0.607 1599 Slack = 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑚𝑚 /𝑢𝑢𝑚𝑚 OLS FE DCCE 0.866*** 0.835*** 0.679*** (0.027) (0.025) (0.033) -0.244*** -0.256*** -0.334*** (0.024) (0.022) (0.024) -0.471*** -0.633*** -1.587*** (0.069) (0.064) (0.275) -0.170*** -0.160*** (0.030) (0.021) -0.170*** -0.160*** (0.030) (0.021) -0.471*** -0.633*** -1.587*** (0.069) (0.064) (0.275) 0.620 0.672 1679 Yes 0.607 0.662 1679 0.607 0.612 1599 Slack = 𝑙𝑙𝑙𝑙(𝑢𝑢𝑚𝑚 /𝑢𝑢𝑁𝑁𝑁𝑁𝑁𝑁 ) OLS FE DCCE 0.872*** 0.843*** 0.672*** (0.028) (0.025) (0.032) -0.241*** -0.252*** -0.336*** (0.024) (0.023) (0.027) - -0.423*** -0.564*** -1.763*** (0.072) (0.065) (0.275) -1.093*** -1.027*** (0.206) (0.159) 0.618 0.674 1679 Yes 0.604 0.665 1679 0.615 0.608 1599 Notes: Standard errors are shown in parentheses. The superscripts *, ** and *** denote significance at the 10%, 5% and 1% levels respectively. FE denotes fixed effects estimators. The dynamic correlated common effects (DCCE) estimates use three lags of the cross section averages. Source: Murphy (2017). 12
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