## Mid-Term Report Summary - MEF (The macroeconomic effects of microeconomic inaction)

The sticky price assumption is central to understand how monetary policy actions propagate to the macroeconomy: absent sticky prices standard models predict that monetary policy is irrelevant for the dynamics of output and other real variables. Yet how to best model price stickiness is an unresolved issue, with relevant macroeconomic consequences. Depending on the details of how stickiness is modeled, the effects of monetary shocks range from being negligible to being substantial. Examples of such different models include: (i) the Taylor model, in which firms keep prices unchanged for a fixed period of time (say six months); (ii) the menu cost model, according to which firms explicitly incur a cost for changing prices (for instance the physical cost of changing the price sticker), and select the timing of their changes in prices weighing cost and benefits of inaction. (iii) the Calvo model, in which there is a constant fixed probability of changing price, independent of the economic environment, and of the time elapsed since the last price change. In the case of a Calvo model the order of magnitude of the cumulative response following a 1% monetary shock is around 0.5% of GDP. In the menu cost model the cumulative output effect is about 6 times smaller. Understanding how to model sticky prices is important, given these large quantitative differences in the predictions for the macro outcomes. The issue is relevant for central banks and other policy institutions who want to improve their macroeconomic models. Our results help choosing between the different models by selecting those whose cross sectional predictions comply with the new and growing microeconomic evidence on price setting behavior. The empirical documentation of price setting patterns using large micro datasets has grown enormously over the past decade. Most interestingly, the recent studies provide information on the distribution of the timing and sizes of price changes. The last generation of sticky price models takes this evidence seriously and uses it as a model selection device: models that are inconsistent with these cross-sectional data are discarded.

Our project constructs models that are able to reproduce such cross-sectional evidence. A key feature of the theoretical models we build is (i) they embed several classic models as special cases and (ii) they retain enough tractability to allow studying the output effects of a monetary shock analytically. A key result is a simple formula, which applies to a large class of models, and is useful to approximate the total cumulative output effect of a small unexpected monetary shock. The formula states that the cumulative output effect of a monetary shock depends on the ratio between two steady-state statistics: the kurtosis of the distribution of price changes K(∆p) and the average number of price changes per year N(∆p). Formally, given the labor supply elasticity 1/e and a small monetary shock d, the cumulative output effect M, namely the area under the output impulse response function, is given by

M = d K(∆p) / ( 6 e N(∆p) ) (1)

The impact of the frequency N(∆p) on the real output effect echoes a standard result in the “New Keynesian” literature: the stickier prices are, the more the inflation response is muted after a monetary policy shock, and the larger is the output response. It is precisely this result which motivated a large body of empirical literature on measuring the frequency of price changes.

The formula in (1) captures this in a stark fashion: halving the frequency of price change doubles the output response. The main novelty of the formula is that the effect of K(∆p) is equally important.

This formula explains the different results obtained by previous models, such as the examples listed at the beginning, by mapping them into a single observable statistics: the kurtosis. Surprisingly, the formula is able to explain model differences that have been obtained in very different sticky price models within a unified setup. In particular, this formula applies to the 2 main workhorse sticky price models, namely models where the decision rules for price setting are state dependent and models where they are time-dependent. The result suggest that the role of the specific microeconomic assumptions used to model sticky prices is completely summarized by the two observable statistics: K(∆p) and N(∆p) .

This result highlights the importance of measuring the cross-sectional kurtosis as well as the frequency of price changes to learn about the effectiveness of monetary policy. This task has led to new developments in estimating such moments using micro data, which are often affected by measurement errors and unobserved heterogeneity. Our work has produced new suggestions to handle those issues. A preliminary empirical analysis of the US and France datasets suggests the value of Kurtosis, and hence the effect of a monetary shock, is between that predicted by a Calvo and a menu cost model, and overall close to that predicted by a Taylor model. If one were to select a simple model matching the distribution of price changes, the Taylor model would fare well.

Our project constructs models that are able to reproduce such cross-sectional evidence. A key feature of the theoretical models we build is (i) they embed several classic models as special cases and (ii) they retain enough tractability to allow studying the output effects of a monetary shock analytically. A key result is a simple formula, which applies to a large class of models, and is useful to approximate the total cumulative output effect of a small unexpected monetary shock. The formula states that the cumulative output effect of a monetary shock depends on the ratio between two steady-state statistics: the kurtosis of the distribution of price changes K(∆p) and the average number of price changes per year N(∆p). Formally, given the labor supply elasticity 1/e and a small monetary shock d, the cumulative output effect M, namely the area under the output impulse response function, is given by

M = d K(∆p) / ( 6 e N(∆p) ) (1)

The impact of the frequency N(∆p) on the real output effect echoes a standard result in the “New Keynesian” literature: the stickier prices are, the more the inflation response is muted after a monetary policy shock, and the larger is the output response. It is precisely this result which motivated a large body of empirical literature on measuring the frequency of price changes.

The formula in (1) captures this in a stark fashion: halving the frequency of price change doubles the output response. The main novelty of the formula is that the effect of K(∆p) is equally important.

This formula explains the different results obtained by previous models, such as the examples listed at the beginning, by mapping them into a single observable statistics: the kurtosis. Surprisingly, the formula is able to explain model differences that have been obtained in very different sticky price models within a unified setup. In particular, this formula applies to the 2 main workhorse sticky price models, namely models where the decision rules for price setting are state dependent and models where they are time-dependent. The result suggest that the role of the specific microeconomic assumptions used to model sticky prices is completely summarized by the two observable statistics: K(∆p) and N(∆p) .

This result highlights the importance of measuring the cross-sectional kurtosis as well as the frequency of price changes to learn about the effectiveness of monetary policy. This task has led to new developments in estimating such moments using micro data, which are often affected by measurement errors and unobserved heterogeneity. Our work has produced new suggestions to handle those issues. A preliminary empirical analysis of the US and France datasets suggests the value of Kurtosis, and hence the effect of a monetary shock, is between that predicted by a Calvo and a menu cost model, and overall close to that predicted by a Taylor model. If one were to select a simple model matching the distribution of price changes, the Taylor model would fare well.