زنجیره های تولید و پویایی های کل تعادل عمومی

Recent empirical studies reveal that monetary shocks can cause persistent fluctuations in aggregate output. In this paper, we propose a mechanism to help generate such persistence. Our dynamic stochastic general equilibrium model features a vertical input–output structure, with staggered price contracts at each stage of production. Working through the input–output relations and the timing of firms’ pricing decisions, the model generates persistent fluctuations in aggregate output and the observed patterns of price dynamics following a monetary shock. Output responses are more persistent, the greater the number of stages of production, and the larger the share of intermediate inputs. With a sufficient number of stages, the persistence is arbitrarily large if the share of intermediate inputs is one at all but finitely many stages.

An order for a new computer often initiates a chain of orders for parts. When the order arrives at a computer vendor's desk, the vendor will start contacting suppliers of microchips, processors, hard-drives, monitors, and operating systems. The monitor maker will then contact suppliers of plastic, glass, and electronic components; and the plastic maker will respond by sending out orders to its own suppliers, and so on. The computer itself, once made, is frequently used as an intermediate input in the production of other goods. The production of a final good typically goes through multiple stages of processing. A thesis of this paper is that the multi-stage structure of production can be important for explaining the relationship between money and aggregate economic activity. We show that the vertical input–output structure helps generate persistent fluctuations in aggregate output and the observed patterns of price dynamics following a monetary shock. It is an old idea that, in an industrialized economy the relationship between money, prices, and output is tied to the interdependence of firms at different stages of production. The idea has been presented at least since Means (1935). Here we quote Basu (1995): [Means] presented evidence that different industries had very different patterns of price changes versus quantity changes in the Great Depression. Means showed that simple goods, such as agricultural products, declined heavily in price, while their quantity was almost unchanged. Complex manufactured goods, on the other hand, showed the opposite pattern, with small price changes and consequently huge declines in the quantity of sales. Crude manufactured goods fell somewhere in between. The evidence presented by Means (1935) has led many to conjecture that there are connections between an input–output structure and aggregate fluctuations. For example, Gordon (1990) considers “the input–output table as an essential component in the description of price stickiness”. There is a growing literature of multi-sector models which are intended to explain the transmission of business cycle shocks through a horizontal roundabout input–output structure within a single stage of production. This literature includes Long and Plosser 1983 and Long and Plosser 1987, Hornstein and Praschnik (1997), Horvath 1998 and Horvath 2000 and Dupor (1999), who focus on real shocks; and Basu (1995) and Bergin and Feenstra (2000), who focus on monetary shocks. On the other hand, recent studies confirm Means's observation on the patterns of price changes at different stages of production. For example, Clark (1999) studies a broad range of data sets and finds that “prices at early stages of production respond more to a monetary policy shock than do prices at subsequent stages of production”. (See, also, Gordon (1981), Blanchard (1987), and Hanes (1999).) Yet, little theoretical work has been done to investigate the shock transmission mechanism embodied in a vertical input–output structure, with the notable exception of Blanchard (1983). Blanchard (1983) shows that a simple reduced-form model incorporating a vertical production chain with prices staggered across different stages of processing can generate patterns of price changes similar to those noted by Means (1935). He was concerned with explaining the sluggish adjustment of the price level. More recently, another empirical fact has attracted much attention: the persistent response of aggregate output to a monetary shock (e.g., Gali, 1992; Christiano et al., 1999). Chari et al. (2000) demonstrate the challenge facing traditional models of staggered price contracts in the spirit of Taylor (1980) in accounting for the observed output persistence in a general equilibrium framework. Motivated by this challenge, various mechanisms have been proposed, most of which focus on introducing factor market frictions in the baseline model of Chari et al. (2000).1 In this paper, we propose a new mechanism that helps meet the challenge posted by Chari et al. (2000) while explaining the observed patterns of price dynamics. We construct a model in which the production of a final good goes through multiple stages of processing, as in Blanchard (1983), but in which individuals optimize. In our model, a firm at the first stage of production uses labor as an input, while a firm at a later stage uses both labor and goods produced at the previous stage. Firms behave as imperfect competitors in their output markets and are price-takers in their input markets. Labor market is perfectly competitive. A representative household consumes a basket of goods produced at the final stage and supplies labor to firms at all stages. To obtain analytical solutions in a system of log-linearized equilibrium conditions, we abstract from capital accumulation. This simplification does not alter our basic conclusions.2 To generate real effects of a monetary shock, we assume that pricing decisions are staggered among firms within each stage (e.g., Taylor 1980 and Taylor 1999) and we derive firms’ optimal pricing decision rules in a standard monopolistic competition framework (e.g., Blanchard and Kiyotaki, 1987). Working through the input–output relations among industries across stages and the timing of pricing decisions among firms within each stage, the model generates persistent responses of aggregate output following a monetary shock and replicates the patterns of price adjustments similar to those documented by Clark (1999) and others. The responses of aggregate output are more persistent, the greater the number of stages of production, and the larger the share of intermediate inputs. With a sufficient number of stages, the persistence is arbitrarily large if the share of intermediate inputs is one at all but finitely many stages. The vertical input–output structure is an essential feature of our model in explaining the dynamics of prices and aggregate output following a monetary shock. In a model with a single stage of production (and thus without the vertical input–output structure), prices adjust quickly and there is no real effect of money beyond the initial contract duration (e.g., Chari et al., 2000). This is so because the shock leads to a quick change in the wage rate and hence in the marginal cost for all firms. In our model with multiple stages of production, firms at more advanced stages of processing face smaller changes in their marginal cost and thus have smaller incentives to change their prices than do firms at less advanced stages. Consequently, movements in prices are dampened through the production chain and the response of aggregate output dies out gradually. The intuition behind the price dampening mechanism of the production chain is as follows. Following a monetary shock, the marginal cost for firms at the first stage immediately changes, forcing them to change their prices fully whenever they have the chance to renew contracts. But firms at the second stage do not face a full change in their marginal cost, because the marginal cost of these firms is partly determined by the price index of the first-stage goods and the price index records both the prices newly adjusted and the prices fixed by previous contracts. Thus, these firms do not have an incentive to adjust their prices fully even if they have the chance to renew contracts. Likewise, firms at the third stage face an even smaller change in their marginal cost and thus have an even smaller incentive to adjust their prices, and so on. Therefore, the multi-stage input–output structure creates a “real rigidity” in the sense of Ball and Romer (1990). When the number of stages of production gets larger, the adjustment of the price level becomes more sluggish and the response of aggregate output becomes more persistent. The input–output structure in our model corresponds in a broad sense to the input–output relations identified by Clark (1999), and our model is able to replicate his findings about the basic behaviors of prices across different stages of production following a monetary shock. For instance, our model can explain why the prices of crude materials are more sensitive to a monetary shock than are the prices of primary goods, which in turn are more sensitive than are the prices of semi-finished goods and finished goods, and so on, a pattern documented by Clark (1999). Our model also predicts that, depending on the length of the production chain, movements in the price level such as the CPI can lag behind movements in prices at early stages of production. It thus provides justification for the practice of policy makers and forecasters looking for signs of impending rise in the general price level by concentrating on price movements in some price-sensitive sectors such as the crude material sector. Our result that the magnitude of price stickiness is increasing in the number of stages of production is similar to that of Blanchard (1983), but for different reasons. In his model, pricing decisions are staggered across different stages and firms within each stage are homogeneous. Basu (1995) points out that, “if the pricing decision in Blanchard's model were made state-dependent then, since the ‘first good’ is made without intermediate goods, there would be no increase in price rigidity regardless of the number of stages of production”. Basu's (1995) criticism does not apply to our model since here pricing decisions are staggered among firms within each stage. Under a state-dependent pricing rule, firms at each stage do not have incentives to synchronize their pricing decisions provided that they face different price adjustment costs (e.g., Dotsey 1997 and Dotsey 1999). As long as firms at some stages do not synchronize, the effects of a monetary shock on price adjustments will be dampened through the production chain. The assumption that pricing decisions are staggered is supported by empirical evidence (e.g., Taylor, 1999). Yet, answering the question of why there is staggering rather than complete synchronization is beyond the scope of this paper. In the literature, some progress has been made on this issue. Dotsey et al. (1997) show that introducing heterogeneity of menu costs across firms can result in endogenous staggering. Ball and Romer (1989) demonstrate that staggering is an equilibrium outcome if there are firm-specific shocks that arrive at different time for different firms. Ball and Cecchetti (1988) show that, with imperfect information, firms cannot distinguish between aggregate demand shocks and firm-specific shocks, and thus do not have an incentive to synchronize. Gordon (1990) argues that, in a world with imperfect information, the complexity of the input–output table makes it unlikely for firms to synchronize, since “the typical firm has no idea of the identity of its full set of suppliers when all the indirect links within the input–output table are considered. … [T]he sensible firm just waits by the mailbox for news of cost increases and then … passes them on as price increases”. Clearly, incorporating these elements to make staggering endogenous will make a model intuitively more appealing. But the basic mechanism by which the production chain transmits monetary shocks will stay the same. We describe the model in Section 2, present the results in Section 3, and conclude the paper in Section 4. The proofs of the analytical results are sketched in the appendix.

We have shown that a model with a vertical input–output structure and staggered price contracts at each stage of production can generate persistent fluctuations in aggregate output and the observed patterns of price dynamics following a monetary shock. Output responses are more persistent, the greater the number of production stages, and the larger the share of intermediate inputs. With a sufficient number of stages, the persistence is arbitrarily large if the share of intermediate inputs is one at all but finitely many stages. Our results do not hinge upon the assumption that the production of a good at a given stage uses all goods produced at the previous stage (along with labor services). This assumption is made only for analytical convenience. To dampen the fluctuations of marginal costs across different stages, what matters is that the down-stream firms supplying inputs to an up-stream firm do not change their prices simultaneously. It does not matter whether the input-supplying firms constitute all or just part of the firms at the same stage. 5 That said, it is important to emphasize that we have merely identified the vertical input–output structure as one contributing mechanism that helps generate the observed persistent responses of aggregate output following a monetary shock. We do not claim that it is the only one—it is clearly not. There are other important contributing mechanisms identified in the literature, such as a horizontal roundabout input–output structure (e.g., Basu, 1995; Bergin and Feenstra, 2000) and labor market frictions (e.g., Huang and Liu, 1998). In the present paper, we abstract from these mechanisms in order to isolate the role of the vertical production chain in generating persistence. In our model with a competitive labor market, labor cost changes rapidly in response to the shock, creating an incentive for quick adjustments in prices. Incorporating labor market frictions will dampen the fluctuations in labor cost and, therefore, will make changes in the price level more sluggish and movements in aggregate output more persistent. A sensible quantitative model that aims at matching its statistics to the data should at least take into account all these monetary transmission mechanisms, should incorporate capital accumulation subject to adjustment costs, and should calibrate the shares of labor, capital, and intermediate inputs at each stage of production. Needless to say, in a model like this, we also need to calibrate the number of stages of production (the N in the present model), which calls for a detailed examination of the input–output table. In light of our finding that the input–output structure is a potentially powerful mechanism in propagating monetary shocks, an empirical investigation of the input–output table should be elevated to the top of the research agenda. Casual observations suggests that N is likely to be large. On this, Gordon (1990) pictures the world as “a gigantic n×n matrix, where n is measured in the thousands, if not the millions. … The gigantic matrix represents the real world, full of heterogeneous firms enmeshed in a web of intricate supplier–demander relationships”. In this web, the intricately made computer is perhaps just a tiny node.