2. The Effects of Government Spending with Free Entry
2.2 The Model
2.2.3 The government
where is the shadow price of physical capital. Combining equation (14) with (16) yields the standard Keynes-Ramsey Rule:
C r
C ( ) . (19) In addition, inserting equations (3), (8) and (10) into (5) and (6) yields:
H
At any point in time, the government levies a lump-sum tax to finance its public expenditure. Accordingly, the government’s budget constraint can be expressed as:
16
T
G . (22) 2.2.4 The competitive equilibrium
By substituting equations (7), (20), (21) and (22) into (17), we obtain the economy-wide resource constraint:
G C Y
K . (23) Based on equations (11), (14), (15) and (20), we can solve employment for the instantaneous relationship: The main equations of the symmetric equilibrium of the economy can then be summarized as follows:
2.3 Long-run effects of fiscal policy
In this section we examine the long-run effect of government spending.
Substituting equations (25) and (26) into (27) and (28), the dynamic system of the economy can be expressed as:
AK H
C GGiven an initial government expenditure G , linearizing equations (30) and (31) 0
Based on equation (32), we can infer the trace and determinant of the Jacobian:17
K As pointed out in the literature on dynamic rational expectations models, such as Burmeister (1980), Buiter (1984) and Turnovsky (2000), there exists a unique perfect foresight equilibrium solution if the number of unstable (positive) roots equals the number of jump variables. Since C is the only jump variable in this dynamic system, there exists a continuum of equilibrium paths converging to the steady state if the dynamic system has two real negative roots. With this understanding, the necessary and sufficient condition for generating local indeterminacy in the dynamic system requires that the trace value of the Jacobian be negative and the determinant value of the Jacobian be positive.
According to the above discussion, we are able to formulate the following proposition:18
Proposition 1. The necessary and sufficient condition for local indeterminacy in the dynamic system requires (1a)(1)(1)0.
18 Alternatively, as stated by Benhabib and Farmer (1994), the necessary condition for local indeterminacy requires that the equilibrium wage-hours locus be positively sloped (the slope here is
1
It is clear that the necessary and sufficient condition for local indeterminacy is totally unrelated to the extent of the monopoly power, but closely related to the following factors: the labor share 1a , the degree of returns to production specialization , and the extent of the congestion effect . We in turn examine how the possibility of local indeterminacy is related to each of these factors.
We first discuss the linkage between the possibility of local indeterminacy and the extent of monopoly power. In an influential paper, Benhabib and Farmer (1994) develop a monopolistic competition model and indicate that the condition for local indeterminacy depends crucially upon the extent of monopoly power. Similarly, McKnight (2011) analyzes the necessary condition without free entry in the open economy, and finds that the condition for local indeterminacy is closely related to the degree of monopoly power. In addition, Chang et al. (2011) consider a monopolistic competition model with free entry and conclude that local indeterminacy can easily occur for mild externalities provided that the degree of monopoly power is large.
Departing from their analysis, our study distinguishes increasing returns to specialization from monopoly power and further finds that the necessary and sufficient condition for local indeterminacy is independent of monopoly power.19
The independent result can be explained intuitively. As addressed in the literature on imperfect competition, such as Dixon (1987) and Startz (1989), a higher degree of monopoly power increases monopoly profits for firms and hence increases households’ disposable income. By way of this so-called feedback effect, the degree of monopoly power can govern the transitional dynamics of the economy. Once free entry is allowed, it will result in a zero profit in equilibrium, which implies that the feedback effect from monopoly profits on the household’s behavior is cut off. As a consequence, the condition for local indeterminacy is independent of the monopoly power.
However, the possibility of local indeterminacy is related to the increasing returns to specialization and the extent of the congestion effect . By differentiating the necessary and sufficient conditions for local indeterminacy with respect to and , we have:
19 By differentiating the necessary condition for local indeterminacy with respect to , we have:
0 )]
1 ( ) 1 )(
1
[(
a
0
Our intuitive explanation for the indeterminacy results in equations (35a) and (35b) is borrowed from Guo and Harrison (2004). For ease of presentation, we state the Keynes-Ramsey rule reported in equations (35a) and (35b) in the following discrete-time form:
where denotes the discount factor. When the households generate optimistic expectations regarding having a higher future return on physical capital (i.e., the marginal product of capital, henceforth referred to as MPK ), they will reduce current consumption C for more investment and enjoy higher future consumption t
1
Ct . A higher value of future consumption together with a lower value of current consumption causes the left-hand side of equation (36) to increase.
With a rise in Ct1 and a fall in C , it is clear from equation (36) that a t self-fulfilling equilibrium driven by the agents’ optimistic expectations can emerge when the right-hand side of equation (36) increases. As described above, the additional investment increases the amount of new capital stock Kt1, and Ht1 will rise in response given that both aggregate labor and aggregate capital are complements by nature. Under such a situation, a higher value of causes MPK to increase, while a higher value of causes MPK to decrease. As a consequence, in association with a higher value of , the households’ initial optimistic expectations regarding a rise in MPK are more likely to lead to a rise in MPK . Accordingly, the households’ initial optimistic expectations are more likely to be self-fulfilling, and the economy is more likely to display equilibrium indeterminacy.
With similar intuition, we can infer that, in association with a higher value of , the economy is more unlikely to exhibit equilibrium indeterminacy.
Summing up the above discussion, we can establish the following proposition:20 Proposition 2. In a one-sector RBC model with monopolistic competition and free entry, the necessary and sufficient condition for equilibrium indeterminacy is independent of the monopoly power. Furthermore, the equilibrium indeterminacy becomes easier when increases, while it becomes more difficult when increases.
At the balanced growth equilibrium, the economy is characterized by K C 0. Let us recall that K~
and C~
are the stationary values of K and C, respectively.
Then, from equation (32) we can infer the following result:21 ] 0
Equations (37) and (38) indicate that a fiscal expansion has a positive effect on the level of capital stock and an ambiguous effect on private consumption. The economic intuition behind equation (38) can be well understood by analyzing the following three scenarios.
The first scenario we deal with can be treated as a benchmark case, and is intended for comparison with other scenarios. The benchmark case is concerned with the standard RBC situation where the returns to production specialization are absent ( 0). Under such a situation, as indicated in equations (37) and (38), an expansion in fiscal expenditure leads to an increase in the level of the capital stock and private consumption is likely to remain unchanged as a result of the fiscal shock.
Following a fiscal expansion, the representative household reacts to this fiscal shock by providing more labor supply and accumulating a higher level of capital stock, thereby resulting in a rise in the aggregate output of the final good. Accordingly, an increase in government expenditure financed by a lump-sum tax leads to a reduction
20 In a two-final-good model, Pavlov and Weder (2012) show that the variety effect of the final investment good crucially affects the indeterminacy condition. By introducing the congestion effect of the start-up cost, our model further shows that the condition for equilibrium indeterminacy is independent of the monopoly power but is closely related to the degree of returns to specialization and the congestion effect of the start-up cost.
21 In the Devereux et al. (1996) analysis, fiscal policy is defined as the ratio of government spending to output. In our analysis, however, fiscal policy is defined as the level of government spending. It is obvious that the ratio of government spending to output is not equivalent to the level of government spending when the expansion in output exceeds the fiscal increment.
in consumption from the beginning, but later on this reduction is exactly offset by a rise in aggregate output. Based on this cognition, a fiscal expansion is therefore ineffective in influencing consumption provided that the returns to production specialization are absent. However, this result runs counter to the existing empirical evidence exhibiting the positive co-movement of consumption and income.
We then deal with the second scenario where increasing returns to an expansion in variety ( 0) are present. Under such a situation, as indicated in equations (37) and (38), an expansion in fiscal expenditure has a positive effect on both the capital stock and private consumption. Moreover, an expansion in fiscal expenditure leads to a rise in the number of intermediate goods. Compared with the benchmark case, an additional positive impact on aggregate output stemming from increasing returns to specialization is created. By virtue of the increasing returns to specialization, a rise in aggregate output exceeds an expansion in fiscal expenditure, and hence fiscal expansion crowds in private consumption.
Some recent studies including Chen et al. (2005), Linnemann (2006) and Ganelli and Tervala (2009) are devoted to solving the fiscal policy puzzle. Chen et al. (2005) shed light on the role of productive public expenditure, and find that consumption may be pro-cyclical in relation to aggregate output if infrastructure and labor are technical complements and the degree of complementarity is sufficiently large.
Linnemann (2006) considers the non-separability between consumption and leisure in the utility function and consumption and leisure are substitutes for the representative agent. Based on the assumption of a strong intra-temporal substitution effect between consumption and leisure, Linnemann (2006) finds that government expenditure can boost private consumption.22 Moreover, by introducing public consumption into the household’s utility function and considering non-separability between the public and private consumption, Ganelli and Tervala (2009) show that, in association with a high degree of public-private consumption complementarity, government expansion is more likely to generate a positive effect on private consumption.23 In departing from these studies, this chapter instead lays emphasis on the importance of the role of the returns to production specialization. To be more specific, we show that, in the presence of varied expansion in production, increasing
22 Bilbiie (2009) specifies a general non-separable preference, and finds that higher government spending can stimulate private consumption if and only if the consumption good is inferior.
23
returns to production specialization can serve as a plausible vehicle to explain the positive response of consumption to the fiscal shocks found in empirical studies.
One point should be emphasized here. In their previous study, Devereux et al.
(1996) specify a parameter to capture both the returns to production specialization and the degree of monopolistic competition. With such a specification, they obtain two important results. First, “the impact of government spending on long-run consumption [crucially] depends not only on the markup, but also on the [labor supply elasticity].” (p. 244). Second, fiscal spending may raise private consumption provided that the degree of monopoly power is large. By contrast, this chapter specifies two distinct parameters to reflect the returns to production specialization and the degree of monopolistic competition, respectively. We unambiguously show that, when the production process is featured with increasing returns to specialization, an expansion in fiscal spending definitely has a positive effect on private consumption regardless of whether the market structure is characterized by monopolistic competition or perfect competition.24 To be more specific, the impact of government spending on long-run consumption is independent of the markup.
The third scenario we deal with is that where decreasing returns to an expansion in variety ( 0) are present. By a similar inference to the second scenario, in the presence of decreasing returns to specialization, a rise in aggregate output falls short of an expansion in fiscal expenditure, and, as a consequence, fiscal expansion partially crowds out private consumption.25
In summing up the above discussion, we can establish the following proposition: Proposition 3. In the presence of increasing returns to specialization ( 0), private consumption will increase in response to fiscal expansions. By contrast, in the presence of decreasing returns to specialization ( 0), private consumption will decrease in response to fiscal expansions.
Moreover, from equations (23), (24) and (36) we can infer the following result:26
24 Proposition 3 is robust even if the intermediate goods market is perfectly competitive.
25 By considering an economy where labor is divisible and production specialization is absent, Lewis (2009) derives a similar result.
26 By setting up a two-sector model with variable returns-to-scale technology, Chao and Yu (1993) examine the effect of fiscal spending in a neoclassical economy. They show that government spending leads to a higher national welfare if the spending results in an increase in the relative price in a higher returns-to-scale sector.
] 0
We can further derive the following expression from equations (3), (5) and (7):
] 0 Equation (40) reveals that a fiscal expansion leads to an ambiguous effect on real wages, depending crucially upon whether the returns to production specialization are increasing or decreasing. Similar to the effect of a fiscal expansion on private consumption, the economic intuition behind equation (40) can also be understood by analyzing the following scenarios.
We first discuss the benchmark scenario where the returns to production specialization are absent ( 0). On the one hand, a fiscal expansion leads to an increase in labor supply as a result of a negative wealth effect. On the other hand, a fiscal expansion leads to a reduction in consumption at the same time, and hence the level of the capital stock will rise over time. Capital accumulation will lead the firms to increase their demand for labor in view of the complementary relationship between labor and physical capital in production. It happens that the rise in labor supply is exactly offset by the rise in labor demand and, as a result, real wages remain intact at the initial level. Accordingly, the impact of real wages is independent of the fiscal shock under such a situation.
We then deal with the second scenario where increasing returns to specialization ( 0) are present. Under such a situation, an expansion in fiscal spending leads to a rise in the number of intermediate goods. Compared with the benchmark case, an additional positive impact on aggregate output stemming from increasing returns to specialization is created and therefore labor demand is increased further than the benchmark case. With an additional positive effect on labor demand, at the initial level of real wages, the rise in labor demand exceeds the rise in labor supply, and hence to restore labor market equilibrium, the new real wage rate should rise in response. Accordingly, in the presence of increasing returns to specialization, real wages are pro-cyclical in response to the fiscal expansion shock. Our theoretical result can be viewed as a possible route to explain the empirical finding that cyclical changes in government spending are associated with positive responses of real wages.
The third scenario we deal with is that where decreasing returns to specialization are present ( 0). Being just the opposite of the second scenario, when compared with the benchmark case, an additional negative impact on aggregate output stemming from decreasing returns to specialization is created. This in turn leads to an additional adverse effect on labor demand. With the additional adverse effect on labor demand, at the initial level of real wages the rise in labor demand falls short of the rise in labor supply, and hence to restore labor market equilibrium, the new real wage rate should fall in response. Accordingly, real wages are countercyclical in response to the fiscal expansion shock when the production process is featured with decreasing returns to specialization. This situation also provides an alternative channel to explain the empirical finding of a negative relationship between real wages and aggregate output. See for instance, Gärtner (2009).
The results in equations (37) and (40) lead us to establish following proposition:
Proposition 4. If the aggregate production function is featured with increasing returns to specialization, real wages are pro-cyclical. However, in the presence of decreasing returns to specialization in production, real wages are countercyclical.27
Finally, from equations (9) and (10) we can derive the following expression:
] 0 Equation (41) represents another novelty for empirical implications of this chapter.
As stated by Devereux et al. (1996, p. 239), “with our specification, all variation in aggregate output is due to entry and exit, as output per firm is unaffected by changes in the aggregate state [and] this implication is, of course, at odds with the fact that output per firm does vary over time.”28 However, the Devereux et al. (1996) finding stands in stark contrast to the empirical observation proposed by, for example, Basu (1995). By endogenizing the start-up cost, this chapter shows that the output level of each intermediate good producer is positively related to the fiscal expansion shock provided that the congestion effect of the start-up cost exists. With this
27 It is worth mentioning that the robustrness of this proposition is independent of the labor supply elasticity. To be more specific, we would derive the same result even if the utility function were specified as UlnCBH1x 1x.
28 This anomalous result also appears in a series of articles, such as Devereux et al. (2000), Chang et al.
(2007) and Chang et al. (2011).
understanding, we establish the following proposition:
Proposition 5. The output level of an individual firm in monopolistic competition is positively related to fiscal expansions, provided that the start-up cost is subject to the congestion effect.
2.4 Conclusion
Most recent empirical studies have pointed out that both consumption and real wages exhibit a positive co-movement with fiscal spending. However, the standard RBC models are incapable of explaining these empirical findings. This chapter thus develops a dynamic general equilibrium macroeconomic model featuring monopolistic competition and a generalized form of the returns to production specialization. Several main findings emerge from the analysis. First, by making a distinction between returns to specialization and monopoly power, this chapter shows that the necessary and sufficient condition for local indeterminacy is independent of the monopoly power but closely related to the degree of returns to specialization and the congestion effect of the start-up cost. Second, in the presence of increasing returns to specialization, private consumption will increase in response to an expansion in government spending. By contrast, in the presence of decreasing returns to specialization, private consumption will decrease in response to an expansion in government spending. Third, when the aggregate production function is featured with increasing returns to production specialization, real wages are pro-cyclical in relation to aggregate output. By contrast, when the aggregate production function is featured with decreasing returns to production specialization, real wages are countercyclical in relation to aggregate output. Fourth, the output level of each intermediate good will increase in response to an expansion in government spending, provided that the start-up cost is subject to the congestion effect.
Chapter 3
Monopoly Power, Endogenous Entry, and Macroeconomic (In)Stability in a Growing Economy
3.1 Introduction
The issue of local indeterminacy or belief-driven fluctuations has been studied extensively in the field of macroeconomics. In their pioneering work, Benhabib and Farmer (1994) propose that local indeterminacy requires a sufficiently high degree of increasing returns to scale in production or sufficiently strong monopoly power.
As pointed out by both Burnside (1996) and Basu and Fernald (1997), the
As pointed out by both Burnside (1996) and Basu and Fernald (1997), the