Academics and policymakers have the central task of evaluating competing models of the macroeconomy (Blanchard 2008). Despite decades of research, there still is no consensus over whether neoclassical, New Keynesian, or other frameworks accurately capture the underlying sources and mechanisms of economic fluctuations.
This disagreement in part reflects a variety of identification and measurement challenges. Different metrics – such as the cyclicality of the labour share (which is typically linked to the inverse of markups), the cyclicality of the household labour wedge, the response of wages and prices to shocks, and fiscal multipliers – lead to conflicting conclusions about which model is most valid.
Research on these metrics is typically done in isolation and the researchers use different empirical settings and designs, and so it is not surprising that there is conflict over how to think about the underlying structure of the economy. Even given a specific metric (the labour share, for example), economists disagree on its cyclicality, with even less consensus on whether the evidence about this metric can be reconciled with evidence on the others.
By focusing on demand shocks, in a recent paper we take a step towards reconciling the facts in providing a comprehensive perspective on how these macro metrics respond to exogenous variation in aggregate demand (Auerbach et al. 2019a). Our approach means we are able to isolate the source of variation driving these macro metrics.
We use city-level data from different sources that contain information on a range of labour-market and goods-market indicators, along with purchases by the US Department of Defense (DoD) – a well-measured, arguably exogenous, and economically important source of variation in demand for local markets – to maximise statistical power and strength of our identification. Our city-level analysis of DoD shocks mean we have a model-free assessment of how macro metrics respond to shocks. To obtain a theoretical benchmark, we simulate various workhorse macroeconomic models. We then compare these with our empirical results to examine how closely the models conform to our estimated responses.
Examining output multipliers suggests whether public spending crowds out private economic activity, a robust prediction of models that feature market clearing. We find a city-level GDP multiplier greater than 1, which is consistent with prior evidence and could imply large national output multipliers (see the discussion in Auerbach et al. 2019b). These would be inconsistent with mainstream neoclassical and New Keynesian models.
But textbook New Keynesian models can accommodate high (relative to neoclassical) multipliers through countercyclical markups, and so we next examine the cyclicality of the inverse of the labour share, which is typically equated with markups. Previous research has agreed on the relevance of the labour share and associated markups for differentiating among macroeconomic modelling frameworks, there has yet to be a consensus on how markups respond to shocks.
The popular proxy for the markup (the inverse of the labour share) is approximately constant or mildly procyclical. Decomposing the change in the labour share into a productivity component (growth in the GDP quantity index relative to growth in hours) and a relative-price component (the growth in producer prices relative to growth in wages), we find that the productivity component moves in the opposite direction of the relative price component.
A DoD spending shock that increases real value-added by 1% increases hours by only 0.57%, indicating a high elasticity of value-added with respect to hours, and thus procyclical productivity, which ceteris paribus drives up the markup. The relative-price component, however, exhibits a reaction in the opposite direction: wages increase relative to producer prices. The net effect of the productivity component and the relative-price component is an approximately acyclical markup, and acyclical labour share.
In isolation, the labour share is only partially informative for distinguishing among macroeconomic frameworks. Galí et al. (2007) and Shimer (2009), among others, argued that the cyclicality of the labour wedge – the ratio between the marginal rate of substitution of consumption for leisure (MRS) and the marginal product of labour (MPN) – is also an important benchmark.
Prior studies have focused on aggregate data and therefore equated worker wages with product wages. Using our data, we can disentangle the two and to examine the effects on the labour wedge more directly. We measure nominal wages by dividing survey respondents’ wage income by the hours they worked in a year. As in Moretti (2011), we measure real worker wages as nominal wages divided by local rental prices (a common proxy for local consumer prices, as housing accounts for approximately 40% of local expenditure).
In response to a DoD-induced increase in local GDP, rental prices increase by more than wages, implying that real (worker) wages fall. At the same time, the shock results in an increase in real product wages, and an increase in local consumption (proxied by auto registrations). The fact that real worker wages fall, while consumption and hours increase, implies a large decline in the labour wedge in response to demand shocks.
This pattern is qualitatively consistent with the countercyclical nature of the aggregate labour wedge that other research has identified (e.g. Shimer 2009). It also has important implications for the mechanisms that account for fluctuations in output and unemployment.
On the cyclicality of the employment rate, we decompose changes in hours into changes in hours per worker, changes in the employment rate (1 minus the unemployment rate), and changes in the labour force. We find that a DoD spending shock increases in the employment rate significantly, accounting for the majority of the adjustment in hours. A part of this employment increase is through firm entry.
Comparing the estimated effects with predictions from macroeconomic models
Table 1 presents the effects of government spending shocks in prominent macro models alongside our empirical estimates. In the table, the neoclassical version of Smets and Wouters (2007) is the version of the model with flexible wages and prices, no variable capital utilisation, and no fixed output cost. In the data estimate of row (5) column (1), the consumer price response is 40% of the estimated land price response (under the conservative assumption that other consumer goods prices are constant). In computing the empirical households labour wedge, we assume GHH preferences (so consumption is irrelevant) and a Frisch elasticity of 1. Separable preferences would result in a much lower household labour wedge, given the strong estimated response of consumption. The empirical consumption response is based on the response of automobile purchases. The household labour wedge in the models is based each model’s parameterisation of the utility function. In the case of Christiano et al. (2016), labour is supplied inelastically, so there is no MRS. Therefore, we compute the labour wedge in that model as we do in the data (as if there were GHH preferences). All responses measure the cumulative reaction of a given variable over one year after a government spending shock, which is equal to 1% of GDP.
Table 1 Comparison of empirical and model-implied moments
Source: Auerbach et al. (2019a).
Each model tends to do well by some metrics but poorly by others:
- The Smets and Wouters (2007) neoclassical model best matches the decline in the real worker wage, but it performs poorly in almost every other dimension. Ffor example, it predicts a massive fall in private consumption (row 9).
- The Smets and Wouters (2007) new Keynesian model performs the best in matching the increase in labour (row 2) due to variable capital utilisation, and it also features a decline in the household labour wedge (due to a falling wage markup) that at least qualitatively matches the empirical estimates. But, similar to the neoclassical model, it predicts a fall in private consumption.
- The Christiano, Eichenbaum and Trabant (2016) model is generally similar to the Smets-Wounters new Keynesian model. It predicts a strong response of the employment rate to a government spending shock.
- Nakamura-Steinsson (2014) with Greenwood et al. (1988) preferences matches the large multiplier (row 1), but it also performs the worst in matching the increase in hours (row 2) and nominal wages (row 3).
A model of excess capacity
Models featuring excess capacity offer a possible rationalisation of our evidence. Extending the model of negligible marginal costs in Murphy (2017) can account for key adjustment margins, and notably can explain a large multiplier, a large increase in local land prices and consumption, a large increase in the employment rate, and a large increase in measured labour productivity. The model is similar in many dimensions to the Michaillat and Saez (2014) theory of idleness, but it differs in the underlying microfoundations.
From a policy perspective, demand stimulus is associated with large benefits when economies operate below capacity, dissipating as economies extend into regions of increasing costs. To gain more detailed insights into the relevant costs and benefits of demand stimulus, it will be important to have quantitative models that are consistent with the facts we were able to document. Extending the negligible marginal cost framework, including dynamic aspects, may be fruitful.
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