David Altig's post at macroblog on the relationship between shocks to the producer price index (PPI) and changes in the (CPI) piqued my interest:
macroblog: The February PPI -- Hot Or Not?: ...A few years back, Jonathon Weinhagen took a look at what we think we know about the relationship between producer prices and broader measures of consumer prices. If terms like "VAR", "variance decompositions", and "impulse responses" mean something to you, you may want to take a look at his article, which appeared in the November 2002 edition of the Monthly Labor Review. If that doesn't sound too interesting to you, here is what Jonathon concluded:
Several authors have investigated the causal relationship between commodity prices and consumer inflation... The common finding in the majority of these studies was that the power of commodity prices to predict CPI inflation has diminished since the 1980s...
To take a quick look at this issue, I downloaded data on real GDP, the federal funds rate, the CPI for all items, the core CPI (less food and energy), the all item PPI, the crude goods PPI, the intermediate goods PPI, and the finished goods PPI from the St. Louis Fed web site (FRED). All data except the federal funds are logged, and the PPI and CPI indices are differenced to obtain inflation rates. Real GDP enters in levels, but using differences does not change the results meaningfully.
These data are used to estimate a VAR model. For those who are unfamiliar with these models, they are general reduced form models of the form:
where L is the number of lags; 2 lags are used here. These models are able, with some assumptions about the underlying structure that aren't apparent from these equations (on that issue, this uses a Choleski decomposition and the ordering is as shown), to show how each variable in the system responds to a shock to other variables. Various definitions of the CPI (all items and core) and the PPI (all items, crude, intermediate, and finished goods) are used. Here are the results showing how the CPI variously defined responds to shocks to each of the definitions of the PPI. The horizontal axis shows the number of quarters after the shock. The graphs are called impulse response functions:
The main result, at least in this particular specification of the empirical model, is that both core and overall inflation (as measured by changes in the CPI or core CPI) are least responsive to shocks to inflation in crude materials prices. In addition, the response of core inflation to shocks to input price inflation is more persistent than the response of overall inflation. The paper David cites notes differences in the results by sample period, and the results shown here are for the entire available sample, 1957:Q1 to 2005:Q4 with allowances for lags, so sub-sample results may show differences. This does, however, agree with the basic result from the paper that shocks to input prices at earlier stages in processing, in this case crude materials, have a smaller impact on output prices than shocks to prices at later stages of production. [Update: Here are the graphs with the growth rate of output used in the model rather than the levels: graph1, graph 2. The results are very similar.]