Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics

The paper explains that its 2003 predecessor was “an early exception” among general equilibrium lumpy-investment models but had “important discrepancies in the model’s microeconomic implications relative to the data”: because that model assumed capital was the sole source of heterogeneity across plants (no persistent plant-specific productivity) and that all nonzero investment incurred the fixed cost, it reproduced only the frequency of positive investment spikes in the data, and did so “only by dramatically overstating the frequency of near-zero (inactive) episodes” – while being structurally unable to generate any negative investment spikes at all, since without idiosyncratic shocks no plant’s capital stock ever exceeds its target.

The paper takes “two important steps away from the first-generation model”: first, allowing “persistent differences across plants not only in their capital stocks but also in their total factor productivities”; second, permitting “plants to undertake low levels of investment without incurring adjustment costs,” formalized as a two-sided generalized (S,s) rule in which a plant can freely adjust capital within a band [ak, bk] around its depreciated capital but must pay a randomly-drawn fixed cost ξ (denominated in labor and redrawn each period from a fixed distribution) to adjust outside that band. The authors motivate the free-adjustment band by noting it is plausible that “fixed adjustment costs apply only to those investments that are comparatively large relative to a plant’s existing capital,” such as building a new structure versus installing a new computer.

Benchmarked against Cooper and Haltiwanger’s (2006) Longitudinal Research Database summary statistics – investment inactivity in only “8 percent of plants on average,” positive investment by “roughly 82 percent of plants” in a typical year, investment spikes (rates exceeding 20% or below -20%) among roughly 20% of plants, with positive spikes “observed 10 times as often as negative spikes” – the paper reports its model is “the first to succeed in matching the average distribution of plant investment rates,” whereas the traditional lumpy model (its own 2003 special case, with no idiosyncratic shocks and no free-adjustment band) “reproduces only one aspect of the micro data, the frequency of positive investment spikes.”

Holding factor prices fixed, the paper reports that “lumpy investment in our model increases skewness roughly 3-fold and kurtosis more than 15-fold relative to the frictionless control,” and that the partial-equilibrium lumpy model exhibits “more than 10 times the variability, and far too little persistence, relative to the aggregate data” – whereas U.S. postwar aggregate investment rates themselves show “near-zero” skewness and excess kurtosis. The paper also documents a sharp asymmetry in the model’s response to shocks: following a two-standard-deviation positive aggregate productivity shock, aggregate capital rises by about 58% in the lumpy model versus 59% in the frictionless model (nearly identical), but following a same-sized negative shock, capital falls by only 20% in the lumpy model versus 37% in the frictionless model – so nonconvex costs “hardly affect” responses to positive shocks while “greatly dampening” responses to negative ones.

The paper’s central result is that equilibrium “dramatically reduces the skewness and excess kurtosis in the distribution of aggregate investment rates, bringing the model far closer to the actual series,” so that “aggregate investment rates exhibit nearly identical volatility, skewness, and kurtosis across the two model economies” (lumpy versus frictionless). Revisiting the same two-standard-deviation shock experiment in general equilibrium, the paper finds aggregate capital now rises by 2.86% (lumpy) versus 2.86% (frictionless) after the positive shock, and falls by 2.53% (lumpy) versus 2.60% (frictionless) after the negative shock – responses that are “far more symmetric” and an order of magnitude smaller than in partial equilibrium, with “no greater asymmetry than occurs in the near-linear frictionless model.”

The paper traces the result to procyclical real interest rates and wages dampening the swings in plants’ target capital stocks that drive aggregate nonlinearities in partial equilibrium: following the positive shock, the (ergodic-weighted) average target capital stock rises “more than 43 percent” in partial equilibrium but only “5.1 percent” in general equilibrium, which in turn limits the rise in the aggregate adjustment rate from 59 percentage points (partial equilibrium) to just 3.6 percentage points (general equilibrium), and the rise in the aggregate investment rate from 59 to 2.9 percentage points. Following the negative shock, the analogous fall in average target capital is 40.4% in partial equilibrium versus 5.5% in general equilibrium, with the aggregate investment-rate decline shrinking from 20.3 to 2.6 percentage points. The authors attribute the dampening to households’ preference for consumption smoothing being enforced through market-clearing: “when we impose market-clearing, this volatility is sharply restrained by procyclical real interest rates, which dampen the changes in target capitals arising from aggregate shocks.”

The paper reports that although “the reallocation of investment goods across plants in response to idiosyncratic shocks is unaffected by equilibrium (as it generates no changes in aggregate investment),” the “micro-elasticity of response to aggregate shocks is greatly reduced when the associated equilibrium movements in relative prices are permitted to feed back into establishments’ decisions.” The authors argue this is a methodologically important point independent of the aggregate results: even though the time-averaged cross-sectional distribution of plant investment rates looks similar whether or not general equilibrium price effects are included, the way that distribution moves in response to an aggregate shock differs sharply – so “equilibrium analysis is essential for understanding investment dynamics even at the most disaggregated level,” and partial-equilibrium estimates of capital adjustment costs from panel data “may be quite sensitive to the assumption about equilibrium.”

Comparing a frictionless model with only idiosyncratic (no fixed-cost) productivity shocks to the same model with fixed adjustment costs added, the paper finds that “these volatile idiosyncratic shocks on their own cause both positive and negative investment spikes in the average year; in fact, these observations are overstated relative to the LRD,” and that adding fixed costs to this environment, “we observe that fixed costs do not cause additional lumpy investments, but instead eliminate some of their occurrences, as indeed is necessary to achieve consistency with the data.” The mechanism is that a plant whose productivity rises knows a fixed cost may be needed to readjust later if its productivity falls again, so “even if it pays its current fixed cost to adopt a new target, the plant’s investment is tempered by an effort to avoid future adjustment costs” – the same caution restraining both positive and negative adjustments, and so reducing (rather than creating) the frequency of extreme investment episodes.

Yes – the paper finds that adding fixed costs to the idiosyncratic-shock model “boost[s] asymmetries in plant-level investment,” increasing the ratio of positive to negative investment spikes, because “depreciation and technological progress automatically erode inactive plants’ effective capital stocks,” so the cost of staying inactive is larger for a plant with too little capital than for one with too much – making plants systematically “less cautious in raising their capital stocks than in lowering them.” The authors draw a cautionary methodological conclusion from this: because investment irreversibilities, or combinations of fixed costs with convex costs, could plausibly generate the same spike-elimination and asymmetry-boosting effects, “there may be no aspect of microeconomic behavior that is uniquely explained by the presence of nonconvex adjustment costs,” making it potentially “virtually impossible to use the establishment investment data to infer the relative size or importance of these costs relative to other frictions.”

The authors note that their model assumes “output is perfectly substitutable across production units,” which makes reallocating production toward high-productivity plants in response to idiosyncratic shocks costless and optimal from the representative household’s perspective – but also “encourages the avoidance of capital adjustment costs through the concentration of investment” in those plants. They conjecture that in an environment where firms instead “produced distinct goods” (so that input reallocation across plants were more costly), more plants would be induced to undertake unconstrained capital adjustment each period, pushing the fraction of adjusting plants “nearer one” and moving the lumpy-investment model’s aggregate behavior “to more closely resemble a linear model with convex capital adjustment costs.”