Topics in the Study of Fluctuations: Business Cycles and Household Formation and Corner Solutions in New Keynesian Models

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AbstractOver time, as people get richer, household size declines: young people move out of their family house earlier, young couples do not live with their parents, older people do not move back with their children, people spend a bigger fraction of their time as singles. A related little known feature is that similar behavior occurs during business cycles: in recessions people tend to live in larger households, while the opposite happens in expansions. This is mostly due to young people in distress moving in with their parents, although there are other margins at work: divorces get delayed, people move in with their siblings or friends. Studies of the business cycles have ignored this margin, and the plan of the first part of the project is to close this gap. Movements in household size over the cycle are important for various reasons. Taking into account that people can move in with others gives a more accurate picture of how willing they are to change the hours that they work over expansions and recessions, and it also gives a very different picture of how good people are at bearing the consequences of economic adversity. So it has potential implicationsboth for the performance of the economy in the aggregate, and for the study of how the effects of business cycles trickle down in the lives of people.The project involves posing artificial economies populated by stable people, those that are older and married, and by not-so-stable people, the young, the unmarried. In these artificial economies, the not-so-stable people have the option of moving in with stable people in certain circumstances that are more prevalent during recessions. The project will then compare the performance of these artificial economies where household size is moving with standard models of the business cycle that ignore this margin and it will measure the adjustments that the latter would need in order to have the main properties of economies with movements in household size. To carry out this type of exercise, there is a need to carefully measure the willingness and ability of people to move in with others. The artificial economies that will be built will have to share with the data the behavior of household composition over the business cycle. Further down the road, the insights provided by the project will be used to construct artificial economies populated by individual agents that form and destroy households (they move out of their parents, get married and divorce, have children who in turn move out) in ways that are similar to those in the U.S., but that are affected by current economic conditions. This feature will be useful as it complements standard artificial economies in the literature where people and households are taken to be either one and the same, or unchanged over time.The project has another part more technical that has to do with the solution methods of some models. The existing methods to solve these models are based on assumptions that certain global considerations are not relevant and use what are called local techniques. Unfortunately, whether these global conditions are satisfied or not are not checked. This part of the project builds global methods that take into account those global considerations. An example of this issue is the following: firms sometimes cannot change the wages of their employees, and they face oscillating demand. What standard methods assume is that these demand oscillations are small and they are accommodated by changing the number of workers hired. It is possible, however that when demand increases are large, there are just not enough workers willing to be hired at those fixed wages (this is the global condition that is assumed not to be violated). Current methods proceed as if there are always available workers, and there are sound reasons to do so when demand increases are small enough. However, sometimes the demand increases are large. The project plans to use methods that accommodate the possibility that workers cannot be found.