Ebook Asset Returns and the Business Cycle in a One Sector Production Economy
Modelling asset prices in a production economy has long been a challenge for students of the business cycle. In particular, as shown by Rouwenhorst (1995), standard dynamic stochastic general equilibrium (DSGE) models with time separable utility usually fail to solve the equity premium puzzle identified by Merha and Prescott (1985), i.e. the fact that the yearly average return to equity exceeds the risk free rate by more than 6%.
In an endowment economy, any trick that increases the volatility of the stochastic discount factor is a potential solution to the equity premium puzzle 5 though some of these tricks might not be empirically credible, e.g. increasing the curvature of the utility function to very high levels. In contrast, in a production economy, consumption is endogenous. Such an environment offers its agents a number a ways of smoothing their consumption path. As a consequence, when utility is time separable, increasing risk aversion does not necessarily result in an increased volatility of the stochastic discount factor. Another challenge emerges that consists in generating sufficiently volatile capital gains. Lettau (2003) and Rouwenhorst (1995) show that standard DSGE models fail to generate enough volatility in these items.
These simple remarks have been the starting point of a growing literature seeking to reproduce asset market facts in business cycle models. In a path breaking contribution, Jermann (1998) asked whether standard, technology driven DSGE models were able to explain not only business cycle but also asset market facts. The answer is 0yes1, as long as the model is augmented with habit formation in consumption and adjustment costs in capital. Though constituting a decisive step forward, JermannGs model is not completely successful and misses a crucial dimension of the business cycle, namely labor market fluctuations.
While Jermann (1998) is silent on this dimension simply because his model abstracts from incorporating a labor decision margin, Boldrin et al. (2001) (BCF hereafter) show that once augmented with a nontrivial labor market equilibrium, the model encounters a number of problems. First, it no longer generates a sizable equity risk premium, unless one assumes that hours have been decided prior to observing the technology shocks. Second, it dramatically fails to mimic the correlation between hours and output at business cycle frequencies. While the latter is strongly positive in the data, it is negative in the model. This unfortunate feature does not depend on whether hours are restricted or not.
In order to overcome the problems raised by this model, BCF (2001) carefully develop a refined supply side structure. They consider a two sector model hit by permanent productivity shocks. In addition to habit formation, their key assumption is that of restricted input mobility. More precisely, they assume that the labor supply and the allocations of labor and capital across the two sectors must be decided prior to observing the shocks. These features help generate volatile equity payoffs and capital gains. Using this model, they are able to replicate a large set of business cycle and asset market statistics. They conclude that their two sector perspective is central to the joint explanation of business cycle and asset market facts in DSGE models.
The present paper takes an opposite stand and simply asks the question: is it possible to offer a joint explanation of business cycle and asset market facts in a one sector stochastic growth model, without predicting grossly counterfactual labor market dynamics? One can view the latter as a refined version of the question initially addressed by Jermann (1998), given our emphasis on labor market dynamics.
Answering this question consists in finding the minimal combination of modeling elements that allows us to replicate the large average equity premium as well as satisfying business cycle dynamics, including labor market facts. The strategy that we find works best consists in mixing habit formation in consumption, dynamic investment adjustment costs and imperfect information in the sense that labor must be decided prior to observing the current period shocks. None of these elements taken alone can help the model reproduce the large equity premium. As shown by Rouwenhorst (1995), limiting the information set available to the agents at the time labor is decided helps increase the equity premium, but not nearly enough to reproduce its empirical counterpart. Similarly, as shown by BCF (1997) increasing the degree of habit formation in consumption does not necessarily solve the equity premium puzzle. In particular, if the model is unable to generate sufficiently volatile capital gains, adding habit persistence to it is of no help. Finally, our own experimentation with dynamic investment adjustment costs shows that increasing these costs does not yield a substantial increase in the equity premium compared to a standard RBC model, which confirms results derived by Jermann (1998) with standard adjustment costs.
However, when combined together, these elements allow us to replicate fairly well (in a formal statistical sense) the equity premium. Given this positive result, we then want to assess whether the model performs well along other dimensions, notably the labor market facts. In the process of doing so, we find that the model encounters troubles reproducing the observed volatility of hours. So as to remedy this problem, we are lead to consider an additional shock, namely a labor supply shock in the form of a shock to laborGs marginal disutility.
The latter can be an important source of fluctuations, as it accounts for persistent shifts in the marginal rate of substitution between goods and work, as suggested by Hall (1997). Such shifts capture persistent fluctuations in labor supply following changes in labor market participation and/or changes in the demographic structure. In the business cycle literature, the effects of these shocks have been studied by a number of authors, including Bencivenga (1992), Kennan (1988), Maliar and Maliar (2004), and others. All find that it plays an important role in explaining labor fluctuations. In particular, as shown by Bencivenga (1992), they permit to generate a negative correlation between hours and productivity (as long as preference shocks are sufficiently important compared to productivity shocks). Notice also that these shocks are observationally equivalent to a tax on labor income and allow us to simply account for other possible distortions on the labor market, such as those labelled labor wedges by Chari, Kehoe and McGrattan (2004).
Of course, we must make sure that incorporating this shock does not deteriorate the modelGs ability to reproduce asset market facts. Unfortunately, this is not warranted. The reason why is simple: in order to reproduce the relative volatility of hours, a large preference shock is needed. However, given a total amount of variance that we want to reproduce, including a stationary preference shock will presumably reduce the contribution of the permanent technology shock to the variance of other variables. At the same time, if we are to reproduce the equity premium, we need a large permanent technology shock in order to generate volatile capital gains. This yields potentially conflicting objectives. We let the data resolve this conflict by resorting to a formal statistical approach.
We estimate and test the model using a standard method of moments. We consider four specifications, depending on whether we allow for restricted labor and/or preference shocks. In each case, we use a small number of over identifying constraints, which we think offer a good summary of the key characteristic of business cycles and asset market facts. To complement this formal assessment of the model, we check its ability to reproduce other key moments not used in estimation. Among these, we pay particular attention to the correlation between average labor productivity and hours. As documented by a large literature and emphasized by Christiano and Eichenbaum (1992), this correlation is small or even negative in the data, while standard technology driven DSGE models usually predict a high and positive correlation.
The remainder is as follows. Section 2 expounds the model, defines the risk free rate and the return to a risky asset, and provides details relating to our model solution and the way in which we compute moments (particularly the average equity premium). In section 3, we describe our formal calibration approach. Section 4 presents our parameters estimates and discusses our results as well as the mechanisms at work in the model. The last section briefly concludes.
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