پویایی های جهانی در یک مدل با جستجو و تطبیق در کار و سرمایه بازار

In this paper global macroeconomic dynamics are studied when search frictions are present in both labor and capital markets. On the basis of the Merz (1995) macroeconomic model with labor market frictions and capital accumulation, our paper offers an extension to frictions in capital markets, analogously modeled as a search and matching process. Using the Merz model as limit case, we consider exogenous as well as endogenous borrowing constraints. We also allow the cost of issuing bonds to change endogenously. As we show, capital market frictions exacerbate and accentuate the interaction between the two markets and magnify the effects of shocks on output, consumption, employment, and welfare. This interaction of the frictions in labor and capital markets are also shown to give rise to multiple equilibria. On the basis of numerical solution techniques, instead of relying on first or second order approximations around a (unique) steady state, our paper uses dynamic programming techniques to compute decision variables and the value function directly and assess the local and global dynamics of the model. The steady state solutions are studied by using the Hamiltonian and the dynamics are assessed for various model variants by using dynamic programming techniques.

Labor market search and matching has been increasingly used in the literature on dynamic stochastic general equilibrium models (DSGE), starting with the seminal paper by Merz (1995) that models labor market frictions in a Real Business Cycle (RBC) model. This approach has proved to be very fruitful to understand the dynamics of output and employment in an intertemporal decision framework. Here consumption, the search effort for jobs by workers, and vacancies posted by firms, are decision variables and both the capital stock and employment are state variables. In this way employment adjustments are costly, and sudden jumps in the employment level of firms are excluded. Nevertheless, the first generation of such search and matching models for the labor market has not been particularly successful in matching empirical facts on volatility of unemployment and vacancies. By modifying the basic model, recent models have performed better in terms of explaining the volatility of unemployment and vacancies (e.g. see Hagedorn and Manovskii, 2008).1 DSGE models have also been extended to include more realistic features of the capital market, such as the financial accelerator. The research on capital markets since the 1980s has pointed out that imperfections and frictions in the capital market prevent supply and demand for financial funds to match easily. Research conducted, for instance, by Bernanke and Gertler (1989) or Stigltiz and Greenwald (2003) demonstrates that there are informational asymmetries and search efforts involved in obtaining credit that makes capital markets behave markedly different from what has been perceived in standard theory. In particular, capital market borrowing may be subject to constraints and financing costs (such as costs to issue new corporate bonds). Those constraints and costs may be given exogenously (from the point of view of the firm) or endogenously, depending on the financial conditions of the firm, such as its net worth. One step toward including more realistic features of capital markets has been to model capital markets in analogy to the labor market as a search and matching process, introducing a market for loanable funds in the spirit of the Wicksellian tradition. Due to such search frictions the supply and demand for bonds are not matched completely and savings may be left unused or there may be an excess demand of savings. Models along this line have recently been developed by Becsi et al. (2000), Den Haan et al. (2003), and Wasmer and Weil (2004). Credit constraints for firms are exogenous in these models since firms credit constraints are given through an aggregate search and matching process. Following this strand of the literature, our model presented here, combines both search and matching in the labor market as well as in the capital market in a model with capital accumulation.2 Yet, going a step further to reflect the work on imperfect capital markets and the financial accelerator, we endogenize financial market frictions and link them to financial conditions of firms. In this context, frictions arising in search and matching are called exogenous financial frictions (exogenous to the firm). On the other hand the frictions arising from collateralized borrowing will be called endogenous financial frictions, since they arise from endogenous credit constraints of firms. We then show that there are exacerbating and accentuating interactions of the two markets that exert—similar to the financial accelerator theory—strong effects on output, consumption, employment, and welfare. In particular, we demonstrate that multiple equilibria and low level steady states can easily arise in such a framework. In contrast to the labor market search literature, in our approach, financial market frictions can significantly alter the global dynamics and global outcomes, possibly leading to severe financial and real contractions.3 In contrast to some recent papers that have used default premia to construct financial accelerator models, we prefer the mechanism of endogenous credit constraints to demonstrate such magnifying mechanism of finance for the real economy. We want to take this as a starting point since the use of default premia in consumption-based macro-economic models is in an early stage and their success is still debated.4 We can justify the use of endogenous credit constraints instead of default premia in such models, as both yield similar results but models based on credit constraints have a more solid base in the academic literature (see, for instance, Grüne et al., 2008a). A further innovation of our paper relates to the numerical solution methodology, which attempts to meet the challenges of the particular characteristics and the out-of-steady-state behavior of such models. Typically, when intertemporal decision models are numerically solved, current approaches have used first or second order approximation methods to solve the model around a (unique) steady state.5 Since in our context the global dynamics needs to be explored we use dynamic programming techniques that allow to better understand the global dynamics of the economy and to account for the possibility of destabilizing mechanisms, bifurcations and multiple steady states.6 Yet, in order to usefully employ dynamic programming it is helpful to explore steady states by the use of the Hamiltonian and the computed steady states thereby. The remainder of the paper is organized as follows. In Section 2 some further literature on search and matching in labor and capital markets are discussed. Section 3 presents our numerical solution technique. Section 4 introduces and solves a basic labor market search and matching model, the Merz (1995) model. Section 5 adds capital market search and matching in addition to the one on the labor market. Hereby the Merz model is considered the limit case of our extended model variants. Section 6 explores the global dynamics of our model variants by using dynamic programming techniques, assuming that credit constraints are exogenous. Section 7 studies two model variants with endogenous credit frictions, the first with endogenous credit constraints and the second with endogenous bond issuing costs. In both cases financial conditions of firms matter when borrowing from capital markets. A final section concludes the paper.

Encouraged by some recent work on a joint modeling of labor and capital market search and matching we started this paper with the modeling of the labor market that follows the Merz (1995) approach and then added capital market search and matching. The latter implies that in addition to the labor market there is also no instantaneous clearing of the capital market. Following recent theories of imperfect capital markets, we have, in addition to exogenous frictions in the capital market, introduced endogenous credit constraints. We also consider endogenous bond issuing costs. As we have shown, these extensions can exacerbate the feedback effects of both markets and negatively impact capital stock, employment, output and consumption. As demonstrated in this paper, the non-linear interactions of the labor market and capital markets are likely to give rise to multiple equilibria and possibly low level steady states. In terms of numerical solution techniques, most of the current approaches have used first or second order approximations around a (unique) steady state. We demonstrate the advantage of using a dynamic programming approach and analyzing the global—rather than local—dynamics in the context of possible multiple steady states. In particular, the use of global dynamic analysis allowed for an understanding of the emergence and disappearance of multiple equilibria depending on the parameter space, and especially the parameter for the severity of capital market frictions. Such an analysis is particularly useful in times of economic and financial stress when small variations in market conditions can lead to abrubt changes in economic dynamics. In this regard, we could assess the effects of both exogenous and endogenous credit constraints as well as endogenous costs of issuing bonds on economic activity and employment. We have solved numerically for the steady state solution(s) by using the Hamiltonian. For selected examples we have also studied the global dynamics of our model variants by using dynamic programming techniques. The use of both the Hamiltonian and dynamic programming have helped us to evaluate our model variants. Overall we could observe, starting with the original Merz model as the limit case for our model extensions, that the introduction of exogenous or endogenous capital market frictions lead to a lower capital stock and reduced employment rates. In particular, this happens when our parameter capturing the strength of the capital market frictions moves down to p1=0.6, the trajectories go down to a lower region of the capital stock and also employment frequently falls. We have shown cases where a global attractor arises at a substantially lower capital stock and lower employment level, though usually the employment is not as much affected as the capital stock. It is a bit of a surprising result, however, that the value function does not necessarily always decline with more frictions, since with lower employment (and higher leisure) welfare can rise. This has often not been realized in other models with frictions in the financial intermediation where the value function is typically not explicitly computed. 43 We also want to note, that the model versions and tools presented here open up the possibility to get a better grasp on monetary policy decisions when capital markets exhibit severe frictions. This is true for both the model variants of exogenous as well as endogenous credit constraints. Easing exogenous credit market frictions by improving the search and matching of financial flows will ameliorate financial market intermediation. Similarly in our model with endogenous credit frictions the improvement of asset values and deleveraging will strengthen firms’ creditworthiness and borrowing capacity and increase capital stock and employment. Also, moving bond issuing costs down in our model version of Section 7.2. This is similar to driving down the credit cost for the borrower as in the model versions by Curdia and Woodford, 2009a and Curdia and Woodford, 2009b. Finally as regards possible further extensions of our approach, these include the introduction of credit constraints for the household sector, which are likely to interact in a mutually reinforcing way with the firm's credit constraints in determining macroeconomic performance. A recent empirical application of our analysis shows promising first results in helping understand how financial frictions induce multiple equilibria and can be tested via a multiple regimes VAR (see Ernst et al., 2010).