Adjustment is Much Slower than You Think

In most instances, the dynamic response of monetary and other policies to shocks is infrequent and lumpy. The same holds for the microeconomic response of some of the most important economic variables, such as investment, labor demand, and prices. We show that the standard practice of estimating the speed of adjustment of such variables with partial-adjustment ARMA procedures substantially overestimates this speed. For example, for the target federal funds rate, we find that the actual response to shocks is less than half as fast as the estimated response. For investment, labor demand and prices, the speed of adjustment inferred from aggregates of a small number of agents is likely to be close to instantaneous. While aggregating across microeconomic units reduces the bias (the limit of which is illustrated by Rotemberg's widely used linear aggregate characterization of Calvo's model of sticky prices), in some instances convergence is extremely slow. For example, even after aggregating investment across all establishments in U.S. manufacturing, the estimate of its speed of adjustment to shocks is biased upward by more than 80 percent. While the bias is not as extreme for labor demand and prices, it still remains significant at high levels of aggregation. Because the bias rises with disaggregation, findings of microeconomic adjustment that is substantially faster than aggregate adjustment are generally suspect.

Price Stickiness in Ss Models: New Interpretations of Old Results

What is the relation between infrequent price adjustment and the dynamic response of the aggregate price level to monetary' shocks? The answer to this question ranges from a one-to-one link (Calvo, 1983) to no connection whatsoever (Caplin and Spulber, 1987). The purpose of this paper is to provide a unified framework to understand the mechanisms behind this wide range of results. In doing so, we propose new interpretations of key results in this area, which in turn suggest the kind of Ss model that is likely to generate substantial price rigidity. The first result we revisit is Caplin and Spulber's monetary neutrality model. We show that when price stickiness is measured in terms of the impulse response function, this result is not a consequence of aggregation, but is due instead to the absence of price-stickiness at the microeconomic level. We also show that the “selection effect,” according to which units that adjust their prices are those that benefit the most, is neither necessary nor sufficient to account for the higher aggregate flexibility of Ss-type models compared to Calvo models. Instead, the key concept is the contribution of the extensive margin of adjustment to the aggregate price response. The aggregate price level is more flexible than suggested by the microeconomic frequency of adjustment if and only if this term is positive.Aggregate price stickiness, adjustment hazard, adjustment frequency,generalized Ss model, extensive margin, Calvo model,strategic complementarities

Missing Aggregate Dynamics: On the Slow Convergence of Lumpy Adjustment Models

The dynamic response of aggregate variables to shocks is one of the central concerns of applied macroeconomics. The main measurement procedure for these dynamics consists of estimmiating an ARMA or VAR (VARs, for short). In non- or semi-structural approaches, the characterization of dynamics stops there. In other, more structural approaches, researcher try to uncover underlying adjustment cost parameters from the estimated VARs. Yet, in others, such as in RBC models, these estimates are used as the benchmark over which the success of the calibration exercise, and the need for further theorizing, is assessed. The main point of this paper is that when the microeconomic adjustment underlying the corresponding aggregates is lumpy, conventional VARs procedures are often inadequate for all of the above practices. In particular, the researcher will conclude that there is less persistence in the response of aggregate variables to aggregate shocks than there really is. Paradoxically, while idiosyncratic productivity and demand shocks smooth away microeconomic non-convexities and are often used as a justification for approximating aggregate dynamics with linear models, their presence exacerbate the bias. Since in practice idiosyncratic uncertainty is many times larger than aggregate uncertainty, we conclude that the problem of missing aggregate dynamics is prevalent in empirical and quantitative macroeconomic research.Speed of adjustment, Discrete adjustment, Lumpy adjustment, Aggregation, Calvo model, ARMA process, Partial adjustment, Expected response time, Monetary policy, Investment, Labor demand, Sticky prices, Idiosyncratic shocks, Impulse response function, Time-to-build

Price Stickiness in Ss Models: New Interpretations of Old Results

What is the relation between infrequent price adjustment and the dynamic response of the aggregate price level to monetary shocks? The answer to this question ranges from a one-to-one link (Calvo, 1983) to no connection whatsoever (Caplin and Spulber, 1987). The purpose of this paper is to provide a unified framework to understand the mechanisms behind this wide range of results. In doing so, we propose new interpretations of key results in this area, which in turn suggest the kind of Ss model that is likely to generate substantial price rigidity. The first result we revisit is Caplin and Spulber's monetary neutrality model. We show that when price stickiness is measured in terms of the impulse response function, this result is not a consequence of aggregation, but is due instead to the absence of price-stickiness at the microeconomic level. We also show that the "selection effect," according to which units that adjust their prices are those that benefit most, is neither necessary nor sufficient to account for the higher aggregate flexibility of Ss-type models compared to Calvo models. Instead, the key concept is the contribution of the extensive margin of adjustment to the aggregate price response. The aggregate price level is more flexible than suggested by the microeconomic frequency of adjustment if and only if this term is positive.

Lumpy Investment in Dynamic General Equilibrium

Microeconomic lumpiness matters for macroeconomics. According to our DSGE model, it is responsible for 92 percent of the smoothing in the investment response to aggregate shocks, and it introduces important nonlinearities and history dependance in business cycles and policy sensitivity. General equilibrium forces are responsible for the remaining 8 percent of smoothing and attenuate, but do not eliminate, aggregate nonlinearities. Not only is the lumpy model better micro-founded than the frictionless model, it also represents an improvement in terms of its ability to match conventional RBC moments, since it raises the volatility of consumption and employment to the levels observed in US data. The model also has distinct implications for the economy's response to large shocks and policy interventions. We illustrate these mechanisms by simulating the dynamics of an investment overhang episode. Our main methodological contribution is to develop a calibration procedure that combines data at different levels of aggregation (sectoral and aggregate)Lumpy investment, RBC model,$(S,s)$ model, idiosyncratic and aggregate shocks, sectoral shocks, adjustment costs, inertia, nonlinearities and history dependence, moments matching.

Three Strikes and You.re Out: Reply to Cooper and Willis

Cooper and Willis (2003) is the latest in a sequence of criticisms of our methodology for estimating aggregate nonlinearities when microeconomic adjustment is lumpy. Their case is based on "reproducing" our main findings using artificial data generated by a model where microeconomic agents face quadratic adjustment costs. That is, they supposedly find our results where they should not be found. The three claims on which they base their case are incorrect. Their mistakes range from misinterpreting their own simulation results to failing to understand the context in which our procedures should be applied. They also claim that our approach assumes that employment decisions depend on the gap between the target and current level of unemployment. This is incorrect as well, since the 'gap approach' has been derived formally from at least as sophisticated microeconomic models as the one they present. On a more positive note, the correct interpretation of Cooper and Willis's results shows that our procedures are surprisingly robust to significant departures from the assumptions made in our original derivations.Adjustment hazard, aggregate nonlinearities, lumpy adjustment, observed and unobserved gaps, quadratic adjustment

Explaining Investment Dynamics in U.S. Manufacturing: A Generalized (S,s) Approach

In this paper we derive a model of aggregate investment that builds from the lumpy microeconomic behavior of firms facing stochastic fixed adjustment costs. Instead of the standard (S,s) bands, firms' optimal adjustment policies are probabilistic, with a probability of adjusting (adjustment hazard) that grows smoothly with firms' disequilibria. Depending upon the specification of the distribution of fixed adjustment costs, the adjustment hazards approach encompasses models ranging from the very non-linear (S,s) model to the linear partial adjustment model. Except for the latter extreme, the processes for aggregate investment obtained from adding up the actions of firms subject to aggregate and idiosyncratic shocks, is highly non-linear. Estimating the aggregate model by maximum likelihood, we find clear evidence supporting non-linear models over linear ones for postwar sectoral U.S. manufacturing equipment and structures investment. For a given sequence of aggregate shocks, the nonlinear model estimated generates brisker expansions and - to a lesser extent - sharper contractions than its linear counterpart. These features fit well the observed positive skewness and large kurtosis of U.S. manufacturing sectoral investment/capital ratios.

Dynamic (S,s) Economies

In this paper we provide a framework to study the aggregate dynamic behavior of an economy where individual units follow (S,s) policies. We characterize structural and stochastic heterogeneities that ensure convergence of the economy's aggregate to that of its frictionless counterpart, determine the speed at which convergence takes place, and describe the transitional dynamics of this economy. In particular, we consider a dynamic economy where agents differ in their initial positions within their bands and face both stochastic and structural heterogeneity; where the former refers to the presence of (unit specific) idiosyncratic shocks, and the latter to differences in the widths of units' (S,s) bands and their response to aggregate shocks. We study the evolution of the economy's aggregate and the evolution of the difference between this aggregate and that of an economy without macroeconomic friction, where the latter pertains to a situation where individual units adjust with no delay to all shocks. We also examine the sensitivity of this difference to common shocks. For example, in the retail inventory problem the aggregate deviation and sensitivity to common shocks correspond to the aggregate inventory level and its sensitivity to aggregate demand shocks, respectively.

Adjustment Is Much Slower Than You Think

In most instances, the dynamic response of monetary and other policies to shocks is infrequent and lumpy. The same holds for the microeconomic response of some of the most important economic variables, such as investment, labor demand, and prices. We show that the standard practice of estimating the speed of adjustment of such variables with partial-adjustment ARMA procedures substantially overestimates this speed. For example, for the target federal funds rate, we find that the actual response to shocks is less than half as fast as the estimated response. For investment, labor demand and prices, the speed of adjustment inferred from aggregates of a small number of agents is likely to be close to instantaneous. While aggregating across microeconomic units reduces the bias (the limit of which is illustrated by Rotemberg's widely used linear aggregate characterization of Calvo's model of sticky prices), in some instances convergence is extremely slow. For example, even after aggregating investment across all establishments in U.S. manufacturing, the estimate of its speed of adjustment to shocks is biased upward by more than 80 percent. While the bias is not as extreme for labor demand and prices, it still remains significant at high levels of aggregation. Because the bias rises with disaggregation, findings of microeconomic adjustment that is substantially faster than aggregate adjustment are generally suspect.Speed of adjustment, discrete adjustment, lumpy adjustment, aggregation, Calvo model, ARMA process, partial adjustment, expected response time, monetary policy, investment, labor demand, sticky prices, idiosyncratic shocks, impulse response function, Wold representation, time-to-build