The Phillips Cuve in the Long Run
-Generally speaking, inflation and the unemployment rate aren’t related in the long-run. This fits the theory developed in the 1970’s that a “natural” rate of unemployment exists.
Carlos Mercado
November 7, 2017
“William Phillips, a New Zealand born economist, wrote a paper in 1958 titled The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957, which was published in the quarterly journal Economica. In the paper Phillips describes how he observed an inverse relationship between inflation and unemployment in the British economy over the period examined. This relationship became known as the Phillip’s Curve.”
First, does this relationship hold in the United States?
Second, is there more to the relationship than what William Phillips found?
Data uploaded to github
Short Run Perspective & Problems
## $Data
## [1] "Consumer Price Index" "Unemployment Level" "Civilian Labor Force"
## [4] "CPI"
##
## $Year
## [1] 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
## [15] 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974
## [29] 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
## [43] 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
## [57] 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
## [71] 2017
##
## $Month
## [1] 1 2 3 4 5 6 7 8 9 10 11 12## Data Year Month Value
## 0 0 0 0##
## Civilian Labor Force Consumer Price Index CPI
## 276 804 38
## Unemployment Level
## 830## Year Month Civilian Labor Force CPI Unemployment Level Date
## 9 1947 9 NA 22.84 NA Sep 1947
## 10 1947 10 NA 22.91 NA Oct 1947
## 11 1947 11 NA 23.06 NA Nov 1947
## 12 1947 12 NA 23.41 NA Dec 1947
## 13 1948 1 60230 23.68 2034 Jan 1948
## 14 1948 2 NA 23.67 2328 Feb 1948
## 15 1948 3 NA 23.50 2399 Mar 1948## Year Month Civilian Labor Force
## 0.00000000 0.00000000 0.67220903
## CPI Unemployment Level Date
## 0.00000000 0.01425178 0.00000000While Unemployment Levels are available for every year since 1948 and CPI available totally, labor force levels are only recorded for about 1/3rd of the time. Essentially, every third month since 1948.
To get a full picture of the Phillips Curve I want to approach from two angles: - First - using quarterly data (i.e. the 1/3rd of data with all elements) I want to check for a general relationship between inflation (% change in CPI) and unemployment rate (level divided by labor force) in the Long Run.
-Generally speaking, inflation and the unemployment rate aren’t related in the long-run. This fits the theory developed in the 1970’s that a “natural” rate of unemployment exists.
Long run as envelopes of the short run, i.e. Inter-decade phillips curves
Splitting the data by decades to see if any particular time period shows a similar relationship
The 1960s look exactly like a Phillips Curve! 
To do this, I want to do three things:
I want to impute missing civilian labor force values by reverting to the values of the previous quarter. These errors will be small, but worth it, for assessing short term changes in unemployment. Thus, we get Monthly instead of Quarterly data.
Calculate the changes in inflation rate and unemployment rate
Test the significance of their correlation by decade (short run) and in aggregate (long run)
## # A tibble: 6 x 5
## # Groups: Decade [1]
## Unem.Rate inflation Decade dinflation dUnem.Rate
## <dbl> <dbl> <chr> <dbl> <dbl>
## 1 3.38 0.00 40s 0.00 0.00
## 2 3.87 -0.04 40s -0.04 0.49
## 3 3.98 -0.72 40s -0.68 0.11
## 4 3.94 1.36 40s 2.08 -0.04
## 5 3.50 0.80 40s -0.56 -0.44
## 6 3.66 0.58 40s -0.22 0.16
## # A tibble: 8 x 3
## Decade `Correlation of small changes` Significance
## <chr> <dbl> <dbl>
## 1 2000's 0.05 0.59
## 2 2010's -0.06 0.59
## 3 40s -0.27 0.21
## 4 50s -0.07 0.42
## 5 60s 0.07 0.44
## 6 70s -0.03 0.71
## 7 80s -0.26 0.00
## 8 90s 0.05 0.56Generally, no, the 1980s, with a few periods of abnormally high unemployment being the exception. Small changes in inflation were well correlated at high levels of inflation and unemployment.
## # A tibble: 8 x 3
## Decade `Correlation as a whole` Significance
## <chr> <dbl> <dbl>
## 1 2000's -0.13 0.16
## 2 2010's 0.11 0.33
## 3 40s -0.28 0.19
## 4 50s -0.12 0.19
## 5 60s -0.56 0.00
## 6 70s -0.14 0.13
## 7 80s -0.10 0.28
## 8 90s 0.12 0.21Generally, no. This relates back to the plot of positive-only inflation. Besides the 1960s, exogenous influences prevent a direct relationship from being predictable.
##
## Pearson's product-moment correlation
##
## data: CPI48dc$dinflation and CPI48dc$dUnem.Rate
## t = -2.1894, df = 828, p-value = 0.02885
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.143177512 -0.007858682
## sample estimates:
## cor
## -0.0758674Yes, Using all the available data, small increases in the inflation rate are significantly correlated with small decreases in the unemployment rate. Breaking it apart by decade, although still 120 data points of monthly data each, reduces our ability to identify statistical significance. This may say something about the natural rates of each statistic.
Yes, a relationship between the two exists. In the long run, small changes in the inflation rate are related to small changes in the unemployment rate.
Uniquely, the relationship was most pronounced in the 1960’s. Afterwards, the same concerns that plagued the theory in the US (the existence of stagflation in the 70s along with high unemployment) muddle the relationship.
Within any one decade, the Phillips Curve hasn’t adequately described the general relationship between the two. This may be due to exogenous influences unique to the decade (e.g. stagflation or changes in government spending).
A change in the what could best be described as the “natural rate” of inflation is related to a change in the “natural rate” unemployment.