How monetary policy affects prices is a classic question in macroeconomics. It has gained new impetus after the recent inflation surge and sharp tightening in monetary policy by the Federal Reserve and other central banks around the world (English et al. 2024). In most macro models, exogenous changes in monetary policy result in both a delayed and a less than one-to-one pass-through to prices. Empirical work on the question yields a range of results on the length of this delay and the size of the pass-through (Ramey 2016). This leaves considerable uncertainty around the question of how long it takes for inflation to come back to its target.
In a recent paper (Aruoba and Drechsel 2024), we shed new light on this question by studying the responses of disaggregated price series to exogenous interest rate changes. Our premise is that a cross-sectional price analysis helps unpack the effect of monetary policy on inflation. If different prices display a different time lag in their peak response, for example, the aggregate series will likely mask this heterogeneity and thus be silent about a potentially important feature of the monetary transmission mechanism. Furthermore, the importance of different price series in aggregate price indices keeps changing, which might alter the transmission of monetary policy over time.
Studying disaggregated prices using local projections and identified monetary policy shocks
We focus on subcomponents of the personal consumption expenditures price index (PCEPI), for two reasons. First, the PCEPI is the price measure targeted by the Fed. Second, the PCEPI can be disaggregated in a way that is relatively consistent through time. The Bureau of Economic Analysis (BEA) provides the PCEPI data at several levels of disaggregation. For example, the roughest level of disaggregation splits prices into prices of goods and services. The finest level of disaggregation that we study in our analysis includes the prices of, for example, corrective eyeglasses and contact lenses, dental services, or water transportation.
Methodologically, we employ a large number of local projections (Jordà 2005) to estimate impulse response functions (IRFs) of different prices to identified exogenous shocks to the target Federal Funds Rate (FFR). We use the identified monetary policy shock series of Aruoba and Drechsel (2022) to analyse plausibly exogenous interest rates changes. We focus on the 1982 to 2008 sample period, during which the Fed targeted the federal funds rate and non-standard monetary policy was not used as a main tool. This choice allows us to draw a connection to monetary policy in 2022 and 2023, which was arguably conducted through ‘traditional’ interest hikes, in the same spirit as those in the pre-zero lower bound period.
The aggregate PCEPI response to a monetary policy tightening
Figure 1 plots IRFs to a one-unit (percentage point) monetary policy contraction. The left panel shows the IRF of the headline PCEPI and the right panel the IRF of the core PCEPI, which excludes food and energy prices. In each case, we plot the response of 100 times the log of the index. The solid line reflects the point estimate, and the shaded areas represent 90% confidence bands based on heteroskedasticity and autocorrelation consistent (HAC) standard errors.
Figure 1 The aggregate response to a monetary policy tightening
The IRF of the headline PCEPI displays a gradual decline, turning significantly negative at conventional levels only after 43 months. The peak reduction occurs after 54 months and our point estimate amounts to a roughly 4% lower price level after a 100 basis point monetary policy contraction, an economically sizeable response. We find a similar timing for the response of the core PCEPI. The magnitude of the response is smaller than for the headline PCEPI, with a point estimate that implies a 2.5% price level reduction after a 100 basis point tightening shock. The lagged patterns in the aggregate price level responses in Figure 1 echo existing findings from the literature.
The responses of PCEPI subcomponents to a monetary policy tightening
Figure 2 plots the IRFs of prices in the third level of disaggregation, which amounts to 15 price subcomponents. The figure reveals quite drastic differences in the price responses to a monetary policy tightening. Some important price categories respond negatively after a long delay or even a positive initial response, while others fall more rapidly. Especially at short horizons, there are differences across categories, with negative, positive, and many flat responses. It is only at longer horizons that the responses of the different price categories start getting more into sync, with many of them becoming significantly negative.
Figure 2 The responses of PCEPI subcomponents to a monetary policy tightening
In particular, we find that important categories such as gasoline, food, and beverages off-premises, and transportation services respond negatively after a long delay. For some components, the initial response to an interest rate increase is even positive, such as for motor vehicles. Other categories, such as clothing and footwear, or recreational goods, fall more rapidly after a contractionary shock. Several durable goods categories tend to respond swiftly. Various categories show responses that are not distinguishable from zero over all horizons. The differences in magnitude across the variables are also substantial. For example, the response of gasoline and other energy products amounts to a reduction of almost 50% in the price level (though the magnitudes are more similar to each other when scaled by the historical standard deviation of each price).
Figure 3 studies the finest disaggregation level considered by our analysis, consisting of 136 different prices. As plotting individual IRFs becomes visually unappealing, we summarise the insights from our analysis of IRFs at this disaggregation level by plotting the fraction of price series that show a significant positive or negative response across horizons. At any given horizon, over 50% of the series show an insignificant response. Early on, the shares of positive and negative responses are roughly the same, leading to the flat response, and then eventually as enough series show a negative response, the overall PCEPI response goes negative.
Figure 3 The share of prices showing a significant positive or negative response across horizons following a monetary policy tightening
In our paper, we discuss interpretations of these findings in light of theories of price adjustment. This discussion highlights that our results are difficult to explain for well-known theories of price adjustment. We point to useful directions for future theoretical research.
Re-aggregation exercises with changing expenditure shares
We also develop a re-aggregation procedure for our cross-sectional IRF estimates and their standard errors. To take into account that the responses of different prices to monetary policy are not independent from each other, we propose a Seemingly Unrelated Regression (SUR) approach to a system of local projections, estimated via Feasible Generalized Least Squares (FGLS). Our SUR approach is a technical contribution to the literature on inference with local projections and could be relevant for other applications in which disaggregated local projections are constructed and aggregation is desired, for example in household-level or firm-level local projections.
With our re-aggregation procedure we study hypothetical aggregate PCEPI responses to a monetary policy change assuming different expenditure shares, such as the expenditure shares over the full sample or those at specific points in history. One experiment that is of particular interest is shown in Figure 4. In the left panel, we re-aggregate our price subcomponent IRFs using the earliest available expenditure weights (1959) and the latest available weights (2023). In each case, we superimpose the PCEPI response based on aggregate data shown in Figure 1.
Figure 4 Re-aggregated PCEPI responses to a monetary policy tightening with different expenditure shares
Comparing the two panels in Figure 4 is informative about whether changing expenditure shares, e.g. due to structural change, have accelerated or decelerated the response of inflation to a change in monetary policy. The figure reveals that the response of inflation to monetary policy is very similar in both cases. Hence, the long-lagged response of prices to monetary policy has not changed due to different consumer expenditure behaviour between 1959 and today.
Discussion: The long and variable lags of monetary policy
Taken together, our results echo the famous insight of Friedman (1960, 1961) that “there is much evidence that monetary changes have their effect only after a considerable lag and over a long period and that the lag is rather variable”. We find that the idea of long lags in the transmission of monetary policy is substantial. We also find large differences in the timing of the response across different variables, which we point out are variable lags in the cross-section of prices.
A corollary of our conclusions is that the price effect of the 2022-23 rate hikes, if hypothetically viewed as a sequence of unanticipated change, would take up to 2026 or 2027 to be fully reflected in the data. In Aruoba and Drechsel (2024), we discuss potential mechanisms through which a faster response than suggested by our estimates might have occurred, by inspecting state-dependence and asymmetries in our local projection setup.
References
Aruoba, B and T Drechsel (2022), “Identifying Monetary Policy Shocks: A Natural Language Approach”, VoxEU.org, 17 May.
Aruoba, B and T Drechsel (2024), “The long and variable lags of monetary policy: Evidence from disaggregated price indices”, CEPR Discussion Paper No. 19175.
English, B, K Forbes and Á Ubide (2024), “Monetary policy responses to the post-pandemic inflation: Challenges and lessons for the future”, VoxEU.org, 14 February.
Friedman, M (1960), A program for monetary stability, Fordham University Press.
Friedman, M (1961), “The lag in effect of monetary policy”, Journal of Political Economy 69: 447–466.
Jorda, O (2005), “Estimation and Inference of Impulse Responses by Local Projections”, American Economic Review 95: 161–182.
Ramey, V A (2016), “Macroeconomic shocks and their propagation”, Handbook of Macroeconomics 2: 71–162.
Romer, C D and D H Romer (2004), “A New Measure of Monetary Shocks: Derivation and Implications”, American Economic Review 94: 1055–1084.
