Unemployment and inflation

Does high unemployment mean that there’s nothing to worry about in terms of inflation?

Since I’ll be trying to answer this question quantitatively using some equations, I’ll begin with some notation. Let ut denote the unemployment rate as of the end of a particular quarter t; currently ut = 9.8 for t corresponding to 2009:Q3. I’ll presume that the question we’re interested in is what sort of inflation rate we should expect over the next two years, and so I’ll let &#960t+8 denote the average inflation rate (quoted at an annual rate) over the next 8 quarters as measured by the price index for personal consumption expenditures (data from FRED). Of course at the current time (t = 2009:Q3) we don’t yet know what the value of &#960t+8 is going to be– that’s what we’re trying to predict.

One way to come up with a prediction is to look at a regression of the historical values of &#960t+8 that we currently know (that is, for t = 1948:Q1 through 2007:Q2) on the historical values of ut. The results from this regression (with Newey-West standard errors in parentheses) and scatterplot of the raw data are given below.


Each circle corresponds to a particular quarter t between 1948:Q1 and 2007:Q2. Horizontal axis: value of unemployment rate in last month of quarter t. Vertical axis: average PCE inflation rate for two years that came subsequent to quarter t. Upward sloping line is the estimated regression relation.

This is of course a version of the famous Phillips Curve, according to which higher rates of unemployment are supposed to be associated with lower rates of inflation. But there’s just one problem– whereas the Phillips Curve is supposed to slope down, the relation we just estimated slopes up. If a given quarter’s unemployment rate was above average, it’s likely that the subsequent inflation rate was above average as well.

The traditional interpretation of this seemingly anomalous result is that there’s another important component of the Phillips relation that was left out of the above regression, which is expectations of inflation. Particularly for the observations from the 1970s and 1980s, people at the time were expecting inflation to remain high. The traditional argument is that if we could add inflationary expectations as a shift variable to the regression, we would see the anticipated negative relation between unemployment and inflation.

One simple way to try to do this is to add lagged values of inflation to the above relation, that is, include &#960t, &#960t-1, and earlier values that would have been known as of quarter t, and see what the contribution of unemployment is to that modified regression. Results of that regression when we add the previous 3 years of inflation observations are given below. Note I haven’t reported the individual estimated coefficients on &#960t, &#960t-1, and &#960t-11 because that exceeds our quota for how many numbers can be reported in an Econbrowser entry.


If you allow for the possibility of changing inflation expectations in this way, the result is that the coefficient on unemployment switches from positive to negative, and the negative coefficient is quite statistically significant. In other words, if we’re going to forecast inflation over the next two years on the basis of what inflation has been over the last three years along with the current unemployment rate, the unemployment rate would enter that forecast with a negative sign– higher unemployment causes us to predict lower inflation.

The forecasts of the above regression (in blue) are compared with the actual values (in black) in the top panel below. We don’t know what the actual values after 2007:Q2 are going to turn out to be yet. But the forecast of the model for the average inflation rate between 2009:Q4 and 2011:Q4 is -0.5%.

Top panel: Black line is the value of subsequent average 2-year inflation rate (&#960t+8) corresponding to each indicated date t Blue line is the predicted value from the dynamic regression for each indicated date t. Bottom panel: unemployment rate as of last month of indicated quarter t.

Does that mean that deflation is the best forecast given the current high level of unemployment and the recent moderate behavior of inflation? It’s certainly not a crazy forecast, given the historical correlations. But the critical question would seem to be whether the contribution of inflationary expectations in the current situation is adequately captured by the recent observed behavior of &#960t.

If for further evidence on inflationary expectations you looked at the gap in yields between nominal Treasuries and TIPS, you’d say inflation expectations remain quite low– currently the 10-year spread corresponds to anu average annual inflation rate under 2% for the next decade.

On the other hand, if your preferred indicator is dollar commodity prices and the sinking exchange rate, the claim that inflationary expectations will remain low is less compelling.

But regardless of where you stand on that question, I believe the Federal Reserve is correct in thinking that high levels of unemployment are a factor that will put downward pressure on inflation over the next two years. The question is how big a pull the dollar and commodities could prove to be in the other direction.

31 thoughts on “Unemployment and inflation

  1. Joseph

    JDH said back in March: “The Fed has declared pretty loud and clear that it is not going to allow deflation. So here’s my personal investment advice: don’t bet against the Fed.” That was good advice.
    Last week Fed governor Kevin Warsh said “Ultimately, when the decision is made to remove policy accommodation further, prudent risk management may prescribe that it be accomplished with greater swiftness than is modern central bank custom.”
    So echoing JDH I would say regarding inflation: “don’t bet against the Fed.”

  2. kharris

    While I think it is mighty nice of you to allow for commodity prices and the dollar to reflect inflationary expectations, we need to recognize that, allowing for liquidity issues, TIPS spreads are a fairly direct measure of inflation expectations, while dollar rates and commodity prices are far from a direct measure. The dollar has a large influence over the price of commodities in dollars. Forced repayment of dollar denominated obligations during the credit and risk perceptions beyond sovereign and inflation risks have had a lot to do with the dollar’s performance.

  3. KevinM

    Eight quarters is a long time. Historical recession UE peaks seem to last only about that long, so of course there would be inflation two years later. Thats when more people are finally finding jobs than losing them, and retail prices can recover. Show the curve with a 4 quarter look into the future.

  4. Meta Finance

    Dear Professor Hamilton,
    Thank you for this analysis.
    However, Im not sure that aggregating data from 1948 to 2009 is the right approach. There have been too many distinctive regimes in that period to draw any robust conclusions.
    For example, over the window from 1965 to 1980 there was a strong positive correlation between unemployment and inflation, due mainly to the stagflationary policies of the time. From 1981 to 1993 there was almost no correlation, reflecting the success of the Volcker Fed in breaking inflationary expectations. And from 1994 to the present the correlation has been negative (albeit small).
    This third period, from 1994 onwards, is to my mind the most interesting. I suspect that a large part of the negative correlation this time round is due to the entry of Chinese labor into global commerce. Chinas entry has reduced the price of retail goods and put downward pressure on first-world wages; hence core measures of inflation have fallen. At the same time Chinas entry has diminished the bargaining power of first-world workers, which is why the last few recessions have been followed by jobless recoveries and persistently anemic employment figures.
    The policy implications of this story are also interesting. In recent years the Fed, reassured by the quiescence in wage and price inflation, and anxious to support the labor market, has kept rates very low for very long periods of time. But the liquidity thus provided did not go into worker compensation or consumer prices (thanks to China). So where did it go? Into asset markets. It is no coincidence that the last few jobless recoveries have been followed by asset market bubbles.
    A more detailed version of this story can be found here:
    Thank you for reading!

  5. Meta Finance

    Thank you for reply. You’re correct, of course. I dug a bit deeper into the numbers myself (using monthly data not quarterly) and agree with you, with the caveat that the relationships I obtain are all rather weak. I still think the China story is insufficiently appreciated as a driver of recent macro events; I would appreciate your thoughts on that. Thanks again!

  6. Bob_in_MA

    Won’t the size/growth of the rest of the world have a much larger impact on future inflation than it did during all other post-war periods?
    The Taylor rule seems to assume that the world economy either is too small to matter, or it mirrors our own.
    But what if world-wide inflation is muted, but the dollar continues it’s slow slide as Asian currencies gain? Commodities could be increasing slightly in rupee terms, but rising 5+% in dollar terms.

  7. spencer

    I have used a very similar approach for inflation expectations to explain the change in average hourly earnings for about 20 years. It has worked extremely well to lead changes in trend and the level of wage growth on a real time basis. This approach is also now forecasting that average hourly earnings growth should be turning negative.
    the equation uses inflation expectations, the unemployment rate, capacity utilization and Nixon–a dummy variable for wage controls.

  8. other

    It seems obvious that the actual chart of inflation precedes the predictions by about a quarter. Doesn’t this destroy the definition of “prediction”?

  9. Laurent GUERBY

    As shown here the unemployment level is drifting over time (1948-2008) relative to the E/P when you select a category of population where everyone should be working (men aged 25-54) :
    4% unemployment in 1948 means 8% jobless, whereas in 2004 a 4% unemployment means 14% jobless.
    So I suggest doing the same graph but using one minus men 25-54 employment rate instead of general unemployment rate to correct for this effect.

  10. Mark A. Sadowski

    A couple of points:
    1) Year on year (yoy) core PCE lags yoy unit labor costs (ULC) fairly reliably by about a year. Yoy ULC has fallen from a high of 3.7% in Q1 2007 to -1.1% as of Q2 2009. In fact ULC plunged 5.0% and 5.9% at an annual rate in the first and second quarters of this year respectively.
    2) The Atlanta fed has this on trimmed CPI:
    “An interpretation of these data is that the September CPI increase was anything but broad-based. Moreover, the data seem consistent with the idea that prices overall are on a path of disinflation. During the first four months of 2009, the majority of the trimmed-mean estimators put retail inflation roughly between 2 percent and 2.3 percent. In the May to August period, most of the estimators were under 1.3 percent. In September, the majority were under 1 percent.”
    In short, yoy ULC has been falling at an average rate of about 0.5% a quarter over the past two years. Meanwhile trimmed monthly CPI has been falling at a rate of perhaps 0.6%-0.7% a quarter this year. Disinflation is already occuring at a disturbingly rapid place in the broader economy, with more likely on the way.

  11. Mike Laird

    Nixon? Inflation is a lot like his famous exit comment to the press. “You’re not going to have me to kick around anymore.”

  12. jedwards

    I respectfully disagree. I’m not an economist but it seems pretty obvious to me that a falling US dollar could very well cause high levels of inflation for the US. This would be a result of the world losing confidence in the US’s ability to recover from the recession in a timely and orderly fashion, which would negatively impact the US dollar.
    Since we no longer produce a lot of our goods and rely on China and other Asian countries, a dropping dollar will instantly cause the cost of our goods to increase. The same goes for oil and other globally-traded commodities.
    This may not be the same type of inflation that your formulae refer to, but to the average citizen, it spends just the same. If a Japanese TV goes from $1000 to $1750, if gas goes to $6/gallon, all prices need to rise in order to account for the simple cost of fuel, transportation, etc.
    If a low US dollar becomes the new norm, it will take years for US factories to start producing our own goods again. This might end up being for the benefit of our economy, but those years in between will be tough.

  13. Meta Finance

    @ jedwards:
    I don’t think Professor Hamilton necessarily believes that weak labor markets will put a lid on inflation. He merely makes the observation that based on historical data, such a forecast is not crazy. He then points out other factors (the dollar, commodities) that may pull the other way.
    (Actually, it’s more subtle than that. Professor Hamilton’s regression uses lagged inflation as a measure of inflation expectations. But there are other ways of measuring inflation expectations. If you look at TIPS spreads, for instance, then these expectations appear well-contained. But if you look at the dollar and commodity prices, the argument is less compelling).
    A few further thoughts on Professor Hamilton’s analysis can be found here:
    Thanks for reading!

  14. RSJ

    “1) Year on year (yoy) core PCE lags yoy unit labor costs (ULC) fairly reliably by about a year. ..”
    ULC is a pretty good proxy for CPI — it doesn’t lag CPI at all, but moves with it. This is because returns to capital tend to be constant, so yoy unit labor costs are basically yoy unit prices; in fact they are a better proxy for CPI than the PCE deflator.
    So the correlation you describe is valid because CPI is trend-following. I wouldn’t necessarily call this due to “inflation expectations”, as CPI is not more trend-following than GDP growth, productivity, the current account, or any of the other big macro variables. This necessarily means that adding a term of the previous year’s X will greatly improve the accuracy of your forecast, but to me this doesn’t necessarily add economic insight.
    The clincher is if your forecast consistently lags the turning points or not. So for example, yoy ULC has turning points at the exact same time as CPI — well sometimes a bit earlier and sometimes a bit later, but generally the turning points occur at the same time.
    I would also add the the “original” Phillips curve was an exponential relationship between the unemployment rate and changes in the *wage-rate*. Not a linear relationship between the unemployment rate and inflation.
    This is a non-linear relationship, in that when unemployment falls from 7% to 6%, the wage rate doesn’t go up (it’s on the “flat” part of the exponential curve), but when it falls from 4.5% to 3.5%, then the wage rate increases much more (as it is on the “steep” part of the curve). Obviously this relationship is not static (i.e. the parameters will change over time), but I wouldn’t say that the parameter shifts depend on expectations of wages so much as on labor market structure; the cost of substituting skilled workers that are in high demand in one geographic area with lower cost labor or labor in another geographic area. As labor becomes more substitutable the steep part of the curve is pushed further out, allowing for lower unemployment without rapidly rising wages. As labor markets become more rigid, then the steep part of the curve is pushed in.
    In general, it’s not at all the case that inflation is a linear function of wage increases. The belief in such a relationship is what led many to interpret the Phillips relation as one between unemployment and inflation, instead of a relationship between unemployment and wage-increases. As wage increases will result in more units sold, the key question is one of unit-labor costs, not labor costs per se.

  15. jcb

    A lot of the analysis of the tradeoff between unemployment and inflation — and of the counter-analysis that relies upon indirect (and highly suspect) inferences about inflation “expectation” from differences in interest and exchange rates — appears to ignore Phillips’ careful qualifications in his 1958 Economica article. That article was a historical piece about unemployment and changing wage rates (not inflation in general) over a particular period (1861-1957) in the United Kingdom. It was not intended as a theory of the relationship between unemployment and inflation of all prices everywhere and at every time! Phillips never said that rising employment is the only factor that accounts for rising wages, and he certainly never said that rising demand for labor is equivalent to (or the cause of?) all price inflation.
    “The purpose of the present study is to see whether statistical evidence supports the hypothesis that the rate of change of money wage rates in the United Kingdom can be explained by the level of unemployment and the rate of change of unemployment, except in or immediately after those years in which there was a very rapid rise in import prices. . . .” (Phillips, 1958)
    In other words, he assumed that a rapid rise in import prices — cost push — could also raise wage rates. In fact, he found several years — 1862, 1919-20, 1940-41, 1950-51 — when increasing import prices did, in fact, account for some or most of the increase in wages, e.g.:
    “a rapid rise in import prices during 1950 and 1951 led to a rapid rise in retail prices during 1951 and 1952 which caused cost of living increases in wage rates in excess of the increases that would have occurred as a result of the demand for labour. . . .”(Phillips, 1958)
    In his conclusion, Phillips does goes on to reaffirm that demand-pull inflation was generally more important than cost-push, with the following caveat: “Ignoring years in which import prices rise rapidly enough to initiate a wage-price spiral, which seem to occur very rarely except as a result of war . . . .”
    Phillips clearly indicates his awareness that both kinds of inflation occurred. Given that the post-1948 US data you use for your own historical regression line includes some eras of old-fashioned cost-push inflation ( limited supply means higher costs), why is trying to construct a mathematical model assuming “expectation-pull” inflation and ignoring other cost and supply factors any improvement over “demand-pull” explanations focusing on employment that also ignore cost and supply factors?

  16. Mark A. Sadowski

    Smackdown duly noted. I should have said “(yoy) core PCE lags yoy unit labor costs (ULC) fairly reliably by about a year IN MY HEAD” (think cost-push inflation).
    Upon reviewing the data and the literature they indeed appear to be (oddly, at least to me) coincident.
    As for what you said about the shape of the Phillips Curve I assume you are making a general statement since I personally said nothing specific about its form.

  17. Robert

    Mark, no real smackdown intended 🙂
    The PC rambling was general, yes. I felt the need to step in to defend Phillips, as I think his reputation has suffered from oversimplification.
    About the ULC — CPI link, my heuristic for this is Kaleckian pricing, e.g. that firms set prices by cost + markup. The mark up term is determined by operational efficiencies and return on capital requirements, and tends to be structural to the sector, so it is less volatile than the cost term. E.g. during a crunch, the firm is more likely to liquidate less efficient operations in order to maintain the markup, rather than accept a lower markup.
    During a boom, the firm is more likely to increase sales rather than prices, up until its costs increase. That is a roughly accurate characterization for most non-crude commodities.
    Going on down the supply chain, you can keep disaggregating to end up with
    price/finished good = sum{markup} + sum{unit labor cost/good}
    where the right hand side is a sum of the markups and ULC for all the intermediate inputs as well as the finished good. Given that the markup term is more stable, CPI changes should be primarily determined by the ULC term.
    Another corollary of this model is that it explains one of Kaldor’s stylized facts, about return on capital being roughly constant in most economies.

  18. pat

    One key variable that is missing from the regression is monetary policy. If one believes that Fed has any influence on inflation, this seems to be one variable that should be included. And this lies my biggest concern: the real fed funds rate (measured as the difference between the nominal fed funds rate and inflation expectations for the next year) is negative, which is a rare event. It happened in the late 70s (followed with inflation out of control), very briefly in the early 90s (got away with that), and in 2003-2004 (followed by overall CPI breach 5% and the biggest financial crisis since GD). And now we are experimenting with it again …

  19. tyaresun

    Is the best analysis possible? I think it would be more realistic to model the infation expectations using other measures than using lagged infation, i.e., use unemployment at time t and inflation expectations at time t to predict future inflation.
    I would suspect that the inflation measured j time periods ago does not capture the quantitative easing that has been unleashed on the economy. Using a more reslistic measure of inflation expectations, particularly one that accounts for the current quantitative easing will give you a much higher inflation forecast.

  20. rookie_parisian

    Robert, in my opinion your cost formula does not include factors like the cost of raw materials and energy, and the cost of debt servicing (to pay back loans for new plants, equipments, expensive acquisition of competitor firms, LBOs, etc). Therefore you jump to the conclusion that the general price level is primarily dependent of unit labor costs, which seems an oversimplification for our modern debt-financed economy, whose growth model is heavily dependent on (cheap) energy prices.
    For a more complete picture of general price level determination, Hyman Minsky had quite interesting propositions (see for example “Stabilizing an Unstable Economy” in which you find price formulas in the “Kaleckian” spirit, but with more components). Minsky tried to enhance basic pricing model to explain the stagflation periods of the 70’s and early 80’s. And this might be exactly where you US citizens are heading for, despite the subdued labor costs. In Europe, I am afraid we may not be so lucky and will not get rid of this mess thanks to a little bit of inflation.
    Thank you all for your interesting comments, in particular the “de-over simplification” of the ideas of Phillips.

  21. Robert

    Hi Rookie,
    Actually, the factors you mentioned are included in this approach. Perhaps I wasn’t clear, but the input goods can themselves be broken up into cost + markup, so you do it for the entire production chain. Factors such as interest and dividend payments are of course return on capital, and are assigned to the markup term. Again, this is a simple toy model meant to serve as a heuristic that explains some observed facts that others may find puzzling, such as the constancy of return to capital for most economies and the relation between ULC and inflation.
    But you are right in that Kalecki was much more sophisticated than this with variable markups as well as market pricing. I certainly don’t want my simple heuristic to be mistaken for the types of models that Kalecki used.

  22. rookie_parisian

    Tyaresun, I agree that if we were able to factor in the impact of money supply we would probably get higher inflation estimates, but the question is how to do this.
    The problem boils down to the old quantity theory of money, and the “P.Q = M.V” well known formula.
    The velocity of money V being extremely volatile, knowing M is just not enough.
    It would be interesting to know if the velocity of money has shown some meaningfull mean-reverting behaviour, if yes then we can reasonably forecast that an increase in M boosts inflation over the long run.
    Or maybe “blindly” add money supply in the model (with some lags) and see if this improves its predictive capacity. But again volatility of V will not help.

  23. Tom

    Inflation is always a worry, but what kind of inflation? We are already seeing powerful inflation in many kinds of assets and commodities.
    On the other hand, the recessionary forces for consumer price deflation are very strong. The peak-to-trough decline in “core” consumer prices after the last major recession (early 80s) was I believe more than 10%. Fed money creation is balancing out that force and keeping consumer prices roughly stable, for now.
    The trouble is that the inflationary forces resulting from money creation continue to work long after the money creation process itself stops. So I expect to see CPI starting around the end of next year, even if monetary policy is tightened before then.

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