Essays on Financial Frictions

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Essays on Financial Frictions by Karl Walentin

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Economics New York University September 2005

Professor Mark Gertler Dissertation Advisor

c Karl Walentin ° All Rights Reserved, 2005

DEDICATION

I dedicate this work to my wife Elizabeth.

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ACKNOWLEDGMENTS

I would like to thank my advisors, Mark Gertler, Sydney Ludvigson and Guido Lorenzoni. Special thanks to Guido for making economic research a fun adventure and Sydney for incredible patience. I am also thankful to Gianluca Violante, Stijn Van Nieuwerburgh, Martin Schneider, Pierpaolo Benigno, Franklin Allen, Kei-Mu Yi, Diego Comin, Charles Himmelberg, Lars Ljungqvist, Kjetil Storesletten, Marc Lieberman and the great faculty at New York University in general for fruitful discussions and seminars. A very warm thank you goes to the economics PhD student community that made these years endurable, even enjoyable. In particular, I would like to thank Luca David Opromolla, Artem Voronov, Alfonso Irarrazabal, Jinyong Kim, Giammario Impullitti, Antonella Trigari, Nestor Azcona and Anastasios Karantounias for good discussions. Finally, I acknowledge financial support from Hedelius-stiftelsen at Handelsbanken (Sweden) for the academic years 2000-2001 and 2001-2002, and New York University for the academic years 2002 to 2005.

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ABSTRACT In the first essay, joint with Guido Lorenzoni, we develop a model of investment with financial constraints and use it to investigate the relation between investment and Tobin’s q. A firm is financed partly by insiders, who control its assets, and partly by outside investors. When insiders’ wealth is scarce, they earn a rate of return higher than the market rate of return, i.e. insiders earn a quasi-rent on invested capital. For incentive reasons, this rent must be paid in the future and is therefore priced into the value of the firm. In this setup Tobin’s q is driven by two forces: changes in the value of invested capital, and changes in the value of the insiders’ future rents. When the firm is hit by a persistent productivity shock the two forces move in the same direction, and we obtain a positive correlation between investment and q. When the firm is hit by a temporary productivity shock the two forces move in opposite directions, the second force dominates, and we obtain a negative correlation between investment and q. We simulate the model and show that when both temporary and persistent shocks are present, investment regressions yield small coeﬃcients on q and large coeﬃcients on cash flow, consistent with the empirical literature. In the second essay we empirically test the Lorenzoni and Walentin (2005) model using three complementary approaches. First, we the test the implication of the model that Tobin’s q theory performs better for sectors with more persistent productivity processes. we do this by running the Fazzari et al. (1988) investment regression on a sample split where firms are grouped according to the persistence of their respective sector productivity. The prediction of the model is confirmed using sector productivity data, but finds no support using firm-level productivity data. Second, we confirm the implication of the model that persistent shocks to productivity, as opposed to temporary shocks, imply a positive comovement between Tobin’s q and investment. Specifically, we show that positive comovement between q and investment indicates that a persistent productivity shock has hit the firm, while a negative comovement indicates a temporary shock. v

Third, we again run the Fazzari et al. investment regression, this time on a sample split where observations are grouped according to their productivity growth, as a proxy for persistent productivity shocks. The predictions of the model are only weakly confirmed when we group using labor productivity growth, but strongly confirmed using sales growth.

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Chapter 1 Financial Frictions, Investment and Tobin’s q1 1.1

Introduction

The standard model of investment with convex adjustment costs predicts that movements in the investment rate should be entirely explained by changes in Tobin’s q. This prediction has generally been rejected in empirical studies. Furthermore, several studies have shown that cash flow and other measures of current profitability have a strong predictive power for investment. This has been taken by many authors as prima facie evidence of the presence of financial constraints at the firm level. Some recent papers – in particular Gomes (2001) and Cooper and Ejarque (2003) – have challenged the above interpretation. These papers compute dynamic general equilibrium models with financial frictions, calibrate them, and look at the relation between Tobin’s q and investment in the simulated series. Gomes (2001) shows that Tobin’s q still explains most of the variability in investment and cash flow does not provide any additional explanatory power. These results seem to echo the concern raised by Chirinko (1993) that, even in the presence of financial constraints, q may still capture the marginal incentive to invest for the individual 1

This chapter is a joint work with Guido Lorenzoni at MIT.

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firm. In his words: “Even though financial market frictions impinge on the firm, q is a forward looking variable capturing the ramifications of these constraints on all the firm’s decisions. Not only does q reflect profitable opportunities in physical investment but, depending on circumstances, q capitalizes the impact of some or all financial constraints as well.”2 In this paper we analyze this issue using a model with a simple financial friction that takes the form of a “collateral constraint”. This type of financial friction has the advantage of being flexible, in that it allows firms to use a rich set of state contingent liabilities, including debt and equity finance. For each firm there is an “insider”, which can be variously interpreted as the entrepreneur, the manager, or the controlling shareholder. Our financial constraint imposes a lower bound on the fraction of the firm’s value held by the insider at each point in time. In this framework, we can explicitly derive the market value of the total outstanding claims on the firm’s future profits. Therefore, we can correctly define the q corresponding to the empirical q obtained from financial market data. We will call this “observed q” as opposed to the “shadow q” that determines the marginal incentive to invest.3 The contribution of this paper is threefold. First, we show that the presence of the financial constraint introduces a wedge between observed q and shadow q. This wedge reflects the tension between the future profitability of investment and the availability of resources in the short run. Second, we show that this wedge can vary over time and thus weaken the observed correlation between q and investment. Third, we show that the equilibrium dynamics of the wedge depend crucially on the persistence of the underlying process for the productivity shocks. In particular, when there are only persistent shocks the wedge tends to be stable over time. This is because when firms face a highly profitable technology in the future they also have more funds to invest in the current period, as current productivity is high. In this case we obtain 2

Chirinko (1993) p. 1903. Apart from the financial friction, our model retains the constant returns to scale assumption and the convex adjustment costs of Hayashi (1982). Shadow q in our model corresponds to Hayashi’s marginal q and is always a suﬃcient statistic for investment. 3

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results similar to Gomes (2001): observed q is, to a first approximation, a suﬃcient statistic for firm’s investment, and cash flow has no extra predictive power. On the other hand, when temporary shocks are present the wedge varies over time. The reason is that financially constrained firms can invest more following a positive temporary shock, even though future productivity is unchanged. In this case firms get closer to their first best capital stock and the wedge between observed q and shadow q decreases. Therefore, when both temporary and persistent shocks are present, it is possible to replicate the low coeﬃcient on q and the high coeﬃcient on cash flow obtained in empirical studies. Using numerical simulations, we show that as the relative importance of temporary shocks increases, the coeﬃcient on q decreases and the coeﬃcient on cash flow increases. In the main part of the paper we concentrate, for simplicity, on firms for which the constraint is always binding in equilibrium. However, the model also bears interesting predictions for firms that are occasionally constrained. These firms will respond diﬀerently to small and large temporary shocks. After large temporary shocks the financial constraint for these firms is slack, they accumulate cash reserves and spread the investment increase over a number of periods. This has two eﬀects: it dampens the impact of a cash flow shock on investment, and it makes the eﬀect more persistent. This is an interesting implication because in our baseline model the coeﬃcient on cash flow tends to be too large, while the serial correlation of investment tends to be too small. Following Fazzari et al (1988) there has been a large empirical literature exploring firm level investment using panel data. The great majority of these papers have found small coeﬃcients on average q and positive significant coeﬃcients on cash flow, or other variables describing the current financial condition of a firm.4 An early critical interpretation of these results was that cash flow contained information regarding future profits that, due to some reason (measurement error or non-fundamental stock market noise), were not captured by the empirically observed q. This interpretation was refuted by Gilchrist and Himmelberg (1995) who showed that cash flow has significant additional predictive power on investment, even after controlling for the 4

E.g. Gilchrist and Himmelberg (1995), Gilchrist and Himmelberg (1998). See Hubbard (1998) for a survey.

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information value in current cash flow.5 The structural models used in the empirical literature typically make simplifying assumptions about the objective of the firm, and take the firm’s financial policy as given. For example, it is typically assumed that a cash-flow shock increases the resources available for investment for a financially constrained firm. However, this depends on the financial policy of the firm, as extra cash flow could also be used to reduce debt, to pay out dividends, or to accumulate reserves. Our approach here is to construct a simple model in which we make explicit the objective of the “insider”, the choice of the financial policy, and the source of the underlying shocks hitting the firm. In this way we derive endogenously the relation between the underlying shocks and the financial position of the firm. The idea of looking at the statistical implications of a simulated model to explain the empirical correlation between investment and q goes back to Sargent (1980). Recently Gomes (2001), Cooper and Ejarque (2001/2003) and Abel and Eberly (2004) have followed this route, introducing either financial frictions or decreasing returns and market power to try to match the existing empirical evidence. The conclusion one reaches from this recent literature is that decreasing returns and market power can generate realistic correlations, while financial frictions do not help in matching the observed correlations. In this paper we show that the second conclusion is unwarranted, and depends crucially on the nature of the underlying shocks. However, there are interesting parallels between our approach and the approach based on decreasing returns. Both approaches imply that movements in q may reflect changes in future rents that may not correspond to changes in current investment. We will discuss this parallel in more detail in the conclusion. The organization of the paper is as follows. Section 1.2 contains a simple two period version of our model illustrating the key mechanism. Section 1.3 contains the setup and the formal analysis of the dynamic model. Section 1.4 describes the calibration and simulation results. In section 1.5 we discuss some variations and extensions of the model. Section 1.6 concludes. 5

This issue is irrelevant for our (or any) theoretical model as for obvious reasons there is no measurement error or stock market noise in the simulated output of the model.

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1.2

A simple example

Consider a simple deterministic two periods economy, populated by a unit mass of entrepreneurs and a unit mass of consumers. Both have linear preferences U (c1 , c2 ) = c1 + c2 . The consumers endowment at date 1 is large enough that in equilibrium the interest rate is zero. Consumers also have a unit endowment of labor in period 2, so that aggregate labor supply L = 1. Entrepreneurs have initial wealth N. An entrepreneur i invests Ki in period 1, and in period 2 produces the consumption good using the Cobb Douglas technology Yi = AKiα L1−α i The firm’s profits in period 2 are © ª − wLi RKi ≡ max AKiα L1−α i Li

where w is the wage rate, to be determined in equilibrium, and R is the gross return on capital, which is equal across firms and depends on w. Suppose the entrepreneurs can credibly commit to pay only a fraction θ of firms’ profits to outside investors in period 2.6 That is, the amount of outside finance that entrepreneur i can raise in period 1 is bounded by θRKi . Thus, investment at date 1 has to satisfy the inequality Ki ≤ θRKi + Ni

(1.1)

Profit maximization at date 2 and market clearing on the labor market imply that in equilibrium 6 See discussion in section 1.3.2. Holmström and Tirole (1997) obtain a similar form for the financial constraint in a model with moral hazard ex post.

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we have RK = αAK α . Let K ∗ denote the first best capital stock, that arises in absence of financial constraints, 1

K ∗ = (αA) 1−α ˆ be the capital stock that satisfies and let K ˆ = αθK ˆ α + N. K

(1.2)

o n ˆ . It is easy to see that In equilibrium total investment at date 1 will be equal to min K ∗ , K

ˆ < K ∗ , the financial constraint is binding in equilibrium, and for small values of N we have K the endogenous value of R will satisfy 1 1 0 If we compute the value of the firm net of these rents we have Vˆ = RK − ((1 − θ) RK − N) = N + θRK = K and using this value we obtain a ratio Vˆ /K = 1. Given that there are no adjustment costs, this would be the “fundamental” value for Tobin’s q. The presence of the financial constraint introduces a wedge between the fundamental value and the value measured on financial markets. Figure 1.1 illustrates the equilibrium described above. The equilibrium level of investment ˆ is given by the point where the curve N + θαAK α intersects the 45o line through the origin. K The corresponding value for q˜ can be determined looking at the slope of the dotted line that ˆ αAK ˆ α ) to the origin. Using this figure we can do two comparative connects the point (K, statics exercises. First, we look at the eﬀect of a change in future productivity A. Figure 1.1 illustrates the eﬀect of an increase in A on investment and q˜. In this case, even though adjustment costs are absent, q˜ and investment move in the same direction. The increase in A has a direct eﬀect on the flow of future profits per unit of capital. This eﬀect tends to increase entrepreneurs’ rents and q˜. On the other hand, the increase in A determines an increase in the value of pledgeable profits and this allows entrepreneurs to expand investment. This eﬀect tends to reduce q˜, because of decreasing returns. However, the first eﬀect dominates and q˜ increases.7 In other 7

˜ to obtain To show this, one can diﬀerentiate equation (1.2) and use the definition of Q ˜= d ln Q

N/K d ln A 1 − α (1 − N/K)

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words, the increase in A increases the level of first best investment, at the same time it increases current resources available for investment. The first eﬀect dominates, and as a consequence the financial constraint becomes tighter in relative terms. This is reflected in a larger value of expected rents, and in higher q˜.

Figure 1.1. Eﬀects of an increase in future productivity, A, on investment and q˜.

Figure 1.2. Eﬀect of an increase in entrepreneurs’ wealth, N, on investment and q˜.

Second, we look at the eﬀect of an increase in entrepreneurs’ initial wealth from N to N 0 . Figure 1.2 illustrates this case. Not surprisingly an increase in entrepreneurs’ wealth increases total investment. At the same time, it reduces the value of observed q˜. This happens because the economy approaches the first best level of capital, and the rents going to entrepreneurs 8

decrease. As these rents decrease, the “mispricing” in the financial value of the firm is reduced and q˜ falls accordingly. Notice that q˜ in this economy reflects the “tightness” of the financial constraint: as entrepreneurs’ wealth increases, the financial constraint in the economy is relaxed and q˜ falls. The first example shows that Tobin’s q can drive movements in investment also in the presence of financial constraints. However, the intuition for this result is quite diﬀerent from the intuition behind Chirinko’s remark. An increase in q˜ is not a reflection of lower financial costs in the future, but of a tighter financial constraint today. The tighter financial constraint reflects an increased gap between desired investment and available resources. In this simple model, movements in A move both investment and the desired (first best) level of capital in the same direction. However, because the desired level of capital changes more, changes in A generate a positive correlation between investment and q˜. On the other hand, movements in N move investment in the same direction and leave the desired level of capital unchanged. Therefore the size of the gap moves in the opposite direction as N , which makes q˜ also move in the opposite direction to N, and this generates a negative correlation between investment and q˜. In the fully fledged dynamic model in the next section, we will see that temporary shocks are analogous to changes in N in our simple two period example. Persistent shocks, on the other hand, are similar to a joint increase in N and A.8 8

Notice that when both A and N are allowed to vary we obtain d ln q˜ =

N/K [d ln A − (1 − α) d ln N ] . 1 − α (1 − N/K)

If we measure the “persistence” of a change in N by d ln A =ρ d ln N we have a positive correlation between investment and q˜ if ρ > (1 − α).

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1.3

The model

In this section we consider a model with convex adjustment costs, constant returns to scale, and a financial friction in the form of a linear collateral constraint. Under these assumptions there is a representative firm in the economy, i.e. all firms choose the same capital-to-labor ratio in equilibrium and are equally constrained. Therefore, there is no interesting cross-sectional dispersion in firms’ economic and financial characteristics. We stay as close as possible to the standard setup with convex adjustment costs à la Hayashi (1982), so that we can identify the role of the financial constraint in determining departures from standard q theory. In particular, we will see that the financial constraint introduces a wedge between the q obtained from financial markets (observed q) and the shadow price used by firms to determine optimal investment (shadow q). In the next section, we will see that the nature of the shocks hitting the economy will be crucial in determining whether this wedge is constant over time or time-varying, and whether it is correlated with cash flow. For expositional purposes, it is useful to concentrate on the time series properties of the model. However, most empirical studies on q theory exploit the variation in investment and q across firms. In section 1.4 and 1.5 we discuss how to interpret the model in terms of its cross-sectional implications.

1.3.1

Setup

There are two groups of agents: consumers and entrepreneurs. Each group is composed of a continuum of agents, with a mass normalized to 1. Consumers are infinitely lived and have linear preferences represented by the utility function E

∞ X

β t Ct

t=0

They have a constant endowment of labor LC that they supply on the labor market each period. Entrepreneurs have linear preferences and a stochastic life span, with constant probability of death γ. Each period a fraction γ of entrepreneurs dies and is replaced by a fraction γ of young entrepreneurs, endowed with LE units of labor in the first period of their life. We

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normalize total labor supply to one, so that LC + γLE = 1. At the beginning of period t a fraction γ entrepreneurs learn that t will be the last period of their life. During period t they are allowed to liquidate all their capital, pay oﬀ their debts, and consume the residual.9 Entrepreneurs’ preferences are described by the utility function Et

∞ X j=0

¡ ¢ e d β j (1 − γ)j (1 − γ) Ct+j + γCt+j

where Cte is consumption in any period before the last, and Ctd is consumption in the last period before death. Entrepreneur i accumulates capital, hires labor, and operates the constant returns to scale technology described by the production function At F (Kit , Lit ) Capital depreciates at rate δ. To install new capital entrepreneurs face the adjustment cost function G (I, K) which is convex in I, homogeneous of degree 1, and satisfies GI (δ, 1) = 1 and GK (δ, 1) = 0. At date t, employing Kito units of old capital and G(Iit , Kito ) units of the consumption good, an entrepreneur can produce Kit+1 units of new capital, ready for production at time t + 1, where Kit+1 = (1 − δ) Kito + Iit . There is a market for used capital goods, or “old capital”, and therefore an entrepreneur can set Kito 6= Kit by purchasing Kito − Kit on the old capital market.10 The price of old capital is denoted by qto . The assumption of a market for old capital is useful to simplify the entrepreneurs’

problem in the last period of their life.11 It also helps in modelling the liquidation proceedings 9

The fact that entrepreneurs die does not aﬀect their discounting as they get a signal of death and have time to consume before dying. This aspect is diﬀerent from some earlier models of financially constrained entrepreneurs. 10 The precise timing is as follows. In each period t first capital is employed together with labor to produce the consumption good, then entrepreneurs trade used capital, then they employ used capital and the consumption good to install new capital for period t + 1. Notice that depreciation occurs after trading of old capital. 11 In this way we avoid assuming that entrepreneurs have to face a large adjustment cost to turn all their capital stock into consumption.

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in the event an entrepreneur diverts the firm’s capital. The only source of uncertainty in the economy is the aggregate level of productivity At . Productivity follows a Markov process, represented by the discrete state space S, the transition probability π (s0 |s), and the function At = A (s). Prices and quantities at date t will be a £ ¤ function of the node st = (s0 , ..., st ). The support of A (s) is denoted by A, A .

1.3.2

Collateral constraint

We now introduce a financial friction in the form of limited enforcement of financial contracts. For simplicity, and without loss of generality, we concentrate on financial contracts that take the form of short term state contingent securities. At node st the entrepreneur sells state contingent promises Di (st+1 |st ) to be paid next period, if node (st , st+1 ) is reached. For brevity we denote Di (st+1 |st ) as Dit+1 . We can think of Dit+1 as reflecting the net present value of

future interest payments and dividend payouts that will go to outsiders after period t. We assume that entrepreneurs have full control over the firms’ assets. At the beginning of each period the entrepreneur can choose to divert part or all of the capital stock. The only recourse creditors have against such behavior is liquidation of the firm. For each unit of diverted capital the entrepreneur is able to capture (1 − θ) units of capital.12 After diversion, the firm is liquidated, the entrepreneur keeps (1 − θ) Kit+1 and can start a new firm.13 Therefore, to

give incentives that prevent diversion the value of the claims held by the insider must be larger than or equal to (1 − θ) times the value of the firm. The value of the firm at date t is given by o At+1 F (Kit+1 , Lit+1 ) − wt+1 Lit+1 + qt+1 Kit+1

where wt denotes the wage rate. 12

Imagine that the entreprenuer sells the capital stock Kt to his brother for 1 dollar and in doing that a fraction θ of the capital is destroyed. Clearly, if an entrepreneur is ever to default it is always optimal for him to divert 100% of the capital before defaulting. 13 For simplicity, we assume that (1 − θ) Kit+1 can still be used for production immediately after default.

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Since diversion is wasteful, we can concentrate on financial contracts that involve no diversion and no liquidation in equilibrium. Then the financial contract must satisfy the no-diversion constraint14 ¡ ¢ o Dit+1 ≤ θ At+1 F (Kit+1 , Lit+1 ) − wt+1 Lit+1 + qt+1 Kit+1

(1.3)

Notice that Dit+1 can capture explicit and implicit features of the “contract” between the insiders and the outside investors. For example, we can consider an equity financed firm in which the dividends and the financial policy are decided by the entrepreneur. Also, the entrepreneur can divert the firm’s capital. The parameter θ captures all the physical and legal barriers that make this diversion costly. In order to guarantee that the entrepreneur follows the promised financial policy and abstains from diversion, the value of the outstanding claims Dit must satisfy (2.1). Most models with limited enforcement consider entrepreneurial firms financed solely with debt, and introduce a condition such as (2.1) to guarantee that the entrepreneur does not default on his debt. Here we make a diﬀerent interpretation that allows us to include equity into Dit , and call “diversion” a major expropriation episode in which the agent controlling the assets of the firm is able to escape with a portion of the firm’s value and leave the firm as an empty shell. In this view, equity and debt are just diﬀerent types of state contingent claims. In this respect, our approach abstracts from corporate finance considerations on the choice between debt and equity. Let m (st+1 |st ) be the stochastic discount factor that is used at date t to price consumption flows at date t + 1. That is, ¡ ¡ ¢ ¢ p st+1 |st = π (st+1 |st ) m st+1 |st is the price of an Arrow security that delivers one unit of consumption at node (st , st+1 ) in 14

An alternative set of assumptions that deliver the same type of constraint is to assume that (1) the entrepreneur loses access to the technology after diversion, (2) diversion is followed by renegotiation, and (3) in the renegotiation stage the entrepreneur makes a take-it-or-leave it oﬀer to the outside investors. With these assumptions, the entrepreneur has all the bargaining power, and whenever Pt+1 Kt+1 > θRt+1 Kt+1 (where P denotes the price of capital paid by the entrepreneurs in this situation) he will renegotiate the value of the debt down to θRt+1 Kt+1 . Apart from the presence of state contingent clauses this is the model used in Kiyotaki and Moore (1997).

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terms of consumption goods at node st . Having assumed that consumers have linear utility in equilibrium we will have m = β. However, for the moment we consider a more general process for m. For brevity we will denote m (st+1 |st ) and p (st+1 |st ) as mt+1 and pt+1 . The entrepreneur takes these state contingent prices as given. If he is selling the state contingent promises Dit+1 and (2.1) is satisfied, these promises are fully credible and their value at date t is Et [mt+1 Dit+1 ] . In a competitive equilibrium entrepreneurs take as given the process for the prices wt , qto and pt , and choose an optimal sequence for Cite , Citd , Kit , Lit and the state contingent promises Di (st+1 |st ), subject to the no-diversion constraint (2.1). The representative consumer takes as given the prices wt and pt and chooses consumption Ct and a portfolio of state contingent one period Arrow securities B (st+1 |st ) at each node st . Entrepreneurs’ and consumers’ choices satisfy market clearing in the labor market, in the goods market, and in the financial market. In particular, market clearing in the financial markets requires Z

1.3.3

¡ ¢ ¡ ¢ Di st+1 |st di = B st+1 |st .

Shadow q and investment

Prior to studying the optimal financial contracts, it is convenient to derive the gross return on capital Rt and the shadow price of new capital. Because of the assumption of constant returns to scale, there is an Rt , identical for all entrepreneurs, that depends on wt and qto , such that Rt Kit = max {At F (Kit , Lit ) − wt Lit + qto Kt } Lit

Notice that entrepreneurs and investors always agree on maximizing the liquidation value of the firm and the no-diversion constraint takes the form Dit+1 ≤ θRt+1 Kit+1 . 14

Entrepreneurs and investors also agree on minimizing the cost of new investment. Again, thanks to the assumption of constant returns to scale, there exists a shadow price of new capital, qt , that depends on qto , such that the minimum cost of investing Kit+1 takes the form min qto Kito + G(Iit , Kito )

qt Kit+1 =

o ,I Kit it

s.t. Kit+1 = (1 − δ) Kito + Iit The solution to this problem implies that every firm chooses the same ratio

(1 − δ) GI In equilibrium the ratios It . Kt

Iit o Kit

µ

Iit o Kit

that satisfies

µ ¶ ¶ Iit Iit o , 1 = qt + GK ,1 Kito Kito

will be equal across entrepreneurs and equal to the aggregate ratio

Therefore, using the envelope theorem, the shadow price of new capital qt satisfies qt = GI

µ

¶ It ,1 . Kt

(1.4)

This is the standard relation between marginal q and investment in a model with convex adjustment costs. This standard relation still holds in our model. Therefore, deviations from q theory must be due to the diﬀerence between this shadow q (q) and the observed q (˜ q), which will be introduced below. Notice that in this model there is a one-to-one relation between qt and qto . Therefore, if the price of used capital was observed, it would be a suﬃcient statistic for total investment. The price qo is the price at which liquidating entrepreneurs sell used capital, so its empirical counterpart are the prices paid for acquisitions and for sales of used capital equipment. This points to a potential alternative way of estimating empirical q that does not rely on financial market data. The presence of this relation, however, relies heavily on the absence of adjustment costs for the transfer of used capital and on the way in which we model firms’ exit. In this model, firms are all identical and exit is an exogenous event, and therefore qo for exiting firms corresponds to qo for all firms. In a more realistic model, the value of q o for exiting firms would

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not be representative of the shadow value for other firms. Therefore, this alternative empirical strategy would be subject to serious problems of measurement error.

1.3.4

Optimal financial contracts

Now we can turn to the determination of the optimal financial contract. The main objective of this subsection is to provide foundations for the simple case in which the financial constraint is always binding (see Proposition 2). Consider an entrepreneur with wealth Nit at the beginning of period t, measured in terms of the consumption good. The available funds for this entrepreneur at date t are Nit + Et [mt+1 Dit+1 ] The entrepreneur’s problem can be described in recursive terms using the value function Vt (Nit ) that denotes the expected utility of a surviving entrepreneur with wealth Nit at the beginning of period t. The Bellman equation characterizing Vt is Vt (Nit ) =

max

e ,K {Dit+1 },Cit it+1

Cite + βEt [γNit+1 + (1 − γ) Vt+1 (Nit+1 )]

Cite + qt Kit+1 ≤ Nit + Et [mt+1 Dit+1 ] Dit+1 ≤ θRt+1 Kit+1 Nit+1 = Rt+1 Kit+1 − Dit+1 Given the linearity of the problem, the value function will have a linear form, Vt (Nit ) = φt Nit , o where φt depends on current and future prices qt+s and wt+s , that are taken as given by the

entrepreneur. The optimal financial contract is characterized by the first order conditions ¡ ¢ ¡ ¢ −β γ + (1 − γ) φt+1 πKit+1 + λ st mt+1 πKit+1 − ¡ ¢ µ st+1 |st = 0 ¤ £¡ ¢ βEt γ + (1 − γ) φt+1 (Rt+1 Kit+1 − Dit+1 ) − ¡ ¢ λ st (qt Kit+1 − Et [mt+1 Dit+1 ]) = 0 16

where λ (st ) is the Lagrange multiplier on the budget constraint and µ (st+1 |st ) is the Lagrange multiplier on the collateral constraint in state st+1 . The envelope condition gives us Vt0 (Nit ) = φt = λt . Consider a node st and an entrepreneur’s decision regarding his financial liabilities in the subsequent node (st , st+1 ). The entrepreneur will compare the marginal value of a dollar today, φt , to the marginal value of a dollar tomorrow in state st+1 . If the following inequality holds for node (st , st+1 )

¡ ¢ β γ + (1 − γ) φt+1 < φt mt+1

(1.5)

then it is optimal to borrow as much as possible in state st+1 and use the proceeds to invest today. In this case we have µ (st+1 |st ) > 0 and the optimal financial contract is given by Dit+1 = θRt+1 Kit+1 . In an equilibrium with mt = β it is possible to prove that (2.2) implies φt > 1 and Cite = 0. Then Kit+1 is given by Kit+1 =

1 Nit qt − θEt [mt+1 Rt+1 ]

for all surviving entrepreneurs. Notice that the ratio m ˜ t+1 = β

γ + (1 − γ) φt+1 φt

represent the shadow discount factor for the entrepreneur, i.e. it represents the ratio of the marginal value of inside wealth tomorrow (in state st+1 ) to the marginal value of inside wealth today. Then, condition (2.2) states that provided that the entrepreneur’s shadow discount factor is smaller than the market discount factor, the entrepreneur will borrow up to his maximum borrowing limit, i.e. the collateral constraint will be binding. In this case we obtain the following recursive condition for φt £¡ ¢ ¤ (1 − θ) βEt γ + (1 − γ) φt+1 Rt+1 φt = qt − θEt [mt+1 Rt+1 ] 17

(1.6)

˜ t+1 represent the rate of return on leveraged entrepreneurial capital Let R ˜ t+1 ≡ R

(1 − θ) Rt+1 qt − θEt [mt+1 Rt+1 ]

then condition (1.6) can be rewritten as the familiar asset pricing expression h i ˜ t+1 = 1. ˜ t+1 R Et m Notice that the market, i.e. the consumers, does not have access to direct investment in entrepreneurial capital, so a similar condition will not hold using the market discount factor. Using (2.2) we can check that h i h i ˜ t+1 > Et m ˜ t+1 = 1. Et mt+1 R ˜ t+1 R This inequality implies that the market return on non-leveraged entrepreneurial capital must also be larger than 1:

∙ ¸ Rt+1 >1 Et mt+1 qt

The diﬀerence E [mt+1 Rt+1 ] /qt − 1 represents an outside finance premium, as it reflects the premium that outsiders would be willing to pay to invest directly in the firms’ capital. In this model, there is a simple relationship between the finance premium and the ratio of inside wealth to total assets invested. Rearranging the entrepreneur budget constraint we obtain

¸ ∙ E [mt+1 Rt+1 ] 1 Nt = 1− qt θ qt Kt+1

(1.7)

A large ratio of inside equity to assets is associated with a small external finance premium. This expression corresponds to (3.8) in Bernanke et al. (2000) that derive it in the context of a model with costly state verification (Townsend (1979)). The advantage of a simple linear collateral constraint is that it simplifies the analysis, and allows us to state explicitly the conditions under which the optimal state contingent contract implies maximum borrowing in every state of the world. 18

1.3.5

Stochastic steady state

It greatly simplifies the analysis to concentrate on stochastic steady states in which the financial constraint is always binding. Proposition 2 below establishes the existence of such a steady state for an economy with “small” productivity shocks. This will form the basis for the numerical analysis in the next section. In section 1.5 we will discuss the more general case in which the financial constraint is occasionally binding. Also, from now on we restrict our attention to economies where in equilibrium Ct > 0 and mt = β. Thanks to the assumption of constant returns to scale, the entrepreneurial sector is easily aggregated. Let Nt denote the aggregate wealth of surviving entrepreneurs at date t, then aggregate capital is given by Kt+1 =

1 Nt qt − βθEt [Rt+1 ]

and the law of motion for Nt is Nt+1 = (1 − γ) (1 − θ) Rt+1 Kt+1 + γwt+1 LE . From these two equations one obtains the following law of motion for the aggregate capital stock Kt+1 =

(1 − γ) (1 − θ) Rt Kt + γwt LE . qt − βθEt [Rt+1 ]

(1.8)

In a stochastic steady state with binding financial constraints, the economy state space is fully described by Kt and st (remember that the state st captures the state of the technology). The stochastic steady state is characterized by the function Kt+1 = K (Kt , st )

19

(1.9)

that satisfies condition (1.8) together with Rt = At FK (Kt , 1) + (1 − δ) GI wt = At FL (Kt , 1)

µ

µ ¶ ¶ It It , 1 − GK ,1 Kt Kt

In a stochastic steady state the process for φt is given by a function φt = φ (Kt , st ) that satisfies conditions (1.6) and (2.2). The solution method for the stochastic steady state is standard. We compute K (Kt , st ) by loglinearizing (1.8). We then solve the resulting diﬀerence equation using the method of undetermined coeﬃcients. Consider the case of a deterministic steady state. Let productivity be constant At = A. In this case, we have qt = 1 qto = 1 − δ ˆ can be derived from (1.8). It is straightforward to show that The steady state capital stock K ˆ is an increasing function of θ.15 The marginal utility of entrepreneurial wealth, φ, is constant K and satisfies φ (1 − θ) βR = γ + (1 − γ) φ 1 − θβR 15

In the case of a Cobb-Douglas production function the steady state capital stock is ˆ = K

µ

αβθ + α (1 − γ) (1 − θ) + γ (1 − α) LE 1 − (βθ + (1 − γ) (1 − θ)) (1 − δ)

20

1 ¶ 1−α

.

therefore condition (2.2) boils down to βR > 1. ˆ we obtain the following Since R is a decreasing function of the steady state level of capital K characterization. Let K ∗ be the first best level of the capital stock, such that β (FK (K ∗ , 1) + (1 − δ)) = 1. Proposition 1 There is a θ∗ ∈ (0, 1) such that if θ ≥ θ∗ the steady state corresponds to the

first best capital stock K ∗ , βR = 1 and the borrowing constraint is not binding. If θ < θ∗ the ˆ < K ∗ , βR > 1 and the borrowing constraint is steady state corresponds to the capital stock K binding.

Having characterized a deterministic steady state, it is possible to characterize the stochastic steady state of an economy with bounded productivity shocks around A. To ensure the stability of the stochastic steady state, it is necessary to impose an additional restriction on the model parameters. Consider an economy with a Cobb-Douglas production function and suppose adjustment costs take a quadratic form: F (K, L) = K α L1−α ξ (I − δK)2 G (I, K) = I + 2 K Now, assume the parameters {α, δ, ξ, θ, γ, LE } satisfy inequality (1.A1) in the Appendix. Then the following proposition holds. Proposition 2 Take an economy with parameters {α, ξ, θ, γ, LE } that satisfy (1.A1). Suppose the economy has a deterministic steady state with βR > 1. Then there is a ∆ > 0 such that if the process for A (s) satisfy A − A < ∆, there exists a stochastic steady state K where the financial constraint is always binding. 21

1.3.6

Asset prices

We will now consider a firm that is financed using equity finance. The majority shareholder (or entrepreneur) keeps 1 − θ of the equity, and sells θ to outsiders. A continuing insider receives a transfer Tt Kt every period and the rest is paid out as dividends. A transfer Tt is needed to allow the insider to capture a higher rate of return on equity than outsiders in every period. We define the market value Vt Kt+1 of the entrepreneurial firms at the end of date t as the market value of the total flow of payments by existing firms. A recursive definition of Vt is Vt = (1 − γ) Et [mt+1 (At+1 FK (Kt+1 , 1) − GK (It+1 /Kt+1 , 1) − Tt+1 + (1 − δ) Vt+1 )] + +γEt [mt+1 (At+1 FK (Kt+1 , 1) − GK (It+1 /Kt+1 , 1) + (1 − δ) qt+1 )] To pin down the financial policy of the firm we will make the following assumption. Assumption I (financial policy). The insider keeps a constant fraction 1 − θ of the firm equity. The transfers {Tt } are designed so that Vt = Et [mt+1 Rt+1 ] . This assumption guarantees that the value of outstanding liabilities θVt Kt+1 is equal to θEt [mt+1 Rt+1 ] Kt+1 so the no-diversion condition is always satisfied. In general, the approach in this paper does not uniquely pin down the financial policy that implements the optimal financial contract. In a separate paper we investigate the implications that this has on the uniqueness of q˜ and on the dependence of q˜ on the firms’ financial policy. For the purposes of the present paper, we work under Assumption I above and keep the financial policy constant. Using this financial policy, we obtain the following expression for observed q˜: q˜t ≡

Vt Kt+1 = E [mt+1 Rt+1 ] Kt+1

22

Let the wedge between observed and shadow q be defined as Ht ≡

q˜t E [mt+1 Rt+1 ] = qt qt

Using (1.7) we can see that there is a one-to-one decreasing relation between the wedge Ht and the inside equity ratio

Nt . qt Kt+1

Thus, we can write the following investment equation It = J (qt ) = J Kt

µ

q˜t Ht

¶

µ = j q˜t ,

Nt qt Kt+1

¶

where J is the inverse of GI (., 1). According to the last equation, investment increases with observed q as well as with the financial ratio

Nt . qt+1 Kt+1

This equation is analogous to equation

(15) in Gomes (2001).

1.4 1.4.1

Aggregate Dynamics Calibration

In this section we examine the quantitative implications of the model, looking at the behavior of investment and q˜ in an economy with binding financial constraints. We use a Cobb-Douglas production function and the quadratic adjustment cost introduced in section 1.3.5. The baseline parameters are α = 0.33;

δ = 0.05;

ξ = 1.1;

β = 0.97; θ = 0.3;

γ = 0.075;

LE = 0.1.

The values for α and δ are standard. Since the time period represents a year, we set β to match a risk-free interest rate of 3%. The adjustment cost ξ is set to 1.1 which is much smaller than the values usually derived from q theory equations. In the absence of financial

23

frictions, the coeﬃcient for q in an investment regression is equal to 1/ξ. Therefore, to match the low value of the coeﬃcient empirically estimated –typically smaller than 0.1– one needs to assume a large value for ξ, which implies unrealistic levels of the average adjustment costs. Setting ξ = 1.1 means that, in absence of financial frictions, the coeﬃcient on q would be close to 1. In our model the choice of ξ will matter mostly because of its eﬀects on the persistence of investment. We will discuss this eﬀect in more detail below. The value for θ is set to 0.3 to match the evidence in Fazzari et al (1988) that 30% of manufacturing investment is financed externally. The parameters γ and LE are chosen to give an outside finance premium close to 3%, similar to the one in Bernanke et al. (2000). For a fixed level of the outside premium, the values of these two parameters have little eﬀect on the results in our simulations. The productivity parameter At is given by At = eat where at follows the process at = xt + η t xt = ρxt−1 + The shocks η t and

t

t

are Gaussian, i.i.d. shocks. Let ρ = 0.9. To apply proposition 2 we need

bounded values for At . This can be achieved by truncating the shocks or by truncating directly the values for At . However, provided that the variances of η t and in which we set bounds for At is immaterial to the results.

24

t

are not too large, the way

1.4.2

Results

The impulse response functions (IRFs) in Figure 1.3 illustrate a crucial implication of our model regarding the eﬀects of temporary and persistent shocks.16 When a persistent shock ( t ) hits the economy, the IRFs in the first column show standard predictions: investment, observed q, and cash flow all jump up and then gradually fall back to steady state values. The collateral constraint gets tighter, as reflected in the increase in observed q. The intuition for this result is as follows. The increased future profitability increases the level of first best capital stock. At the same time, entrepreneurs’ resources increase because they receive extra cash flow today and can increase their leverage, thanks to the increase in pledgeable capital. However, the first eﬀect dominates, given the high persistence of the shock, and this implies that the gap between feasible capital stock and first best capital stock increases. The larger gap corresponds to a tighter financial constraint and a higher observed q. 16

The capital stock and q˜ are reported in log deviations from the non-stochastic steady state. The investment rate variable it corresponds to It − δKt Kt and cash flow (normalized by capital stock) is defined as cft =

At F (Kt , Lt ) − wt Lt αAt Ktα = = αAt Ktα−1 . Kt Kt

25

Persistent shock ε

0.2

i

0

obs. q

-0.2

0

0

5

10

15

-0.1

20

0.5

-4

0

-6

-0.5

Temporary shock η

0.1

0

5

10

15

-8

20

1

-3 0 x 10

5

10

15

20

0

5

10

15

20

0

5

10

15

20

0

5

10

15

20

0.08

k

0.06 0.5 0.04

cf

0

0

5

10

15

0.02

20

0.2

0.2

0

0

-0.2

0

5

10

15

-0.2

20

Figure 1.3. Impulse response functions to persistent and temporary shocks, respectively.

The eﬀects are quite diﬀerent when we look at the temporary productivity shock (η t ), in the second column of Figure 1.3. A temporary shock can be viewed as a pure wealth shock to entrepreneurs, as future profitability is unchanged. The direct result of the shock is that entrepreneurs become less financially constrained, increase their investment and the economy moves closer to the (unchanged) first best capital stock, K ∗ . Accordingly, the gap between the first best capital stock and the feasible capital stock shrinks and observed q falls. Another way to understand the fall in observed q is by noting that the increased capital-labor ratio results in lower return to capital. A negative contemporaneous relationship between investment and observed q holds. All this happens at the impact of the temporary shock. Investment and cash flow then immediately return to steady state values, while the capital stock, and therefore observed q, only gradually return to their long run values. Using these two extreme cases we see that the persistence of the productivity shock aﬀects the sign of the relation between observed q and investment. Cash flow, on the other hand, covaries positively with investment regardless of the persistence of the shock.

26

The importance of the persistence of the productivity shock can be seen by plotting the relation between investment and q˜, and between investment and cash flow. In Figure 1.4 we plot the relationships for an economy with only persistent shocks. There is almost a perfect linear relationship between investment and q˜, and a more noisy relationship between investment

i

and cash flow.

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

0

-0.005

-0.005

-0.01

-0.01

-0.015

-0.015

-0.02 -0.04

-0.02

0

0.02

-0.02 -0.02

0.04

obs. q

-0.01

0

0.01

0.02

cash flow

Figure 1.4. Simulated values for (i, q˜) and (i, cf ), with only persistent shocks. An opposite, and more striking result applies in the case of an economy with only temporary shocks, which is plotted in Figure 1.5. In this case, observed q displays a weak negative relationship with investment, while cash flow has a positive relationship with an almost perfect fit. This picture shows why the model with collateral constraints and temporary shocks can match the empirical results in the investment literature – a low coeﬃcient on q˜ and a large positive coeﬃcient on cash flow (cf ) in standard investment regressions.

27

0.03

0.02

0.025

0.015

0.02 0.01 0.015 0.005

i

0.01

0.005

0

0

-0.005

-0.005 -0.01 -0.01 -0.015

-0.015

-0.02 -0.01

-0.005

0

0.005

-0.02 -0.04

0.01

obs. q

-0.02

0

0.02

0.04

cash flow

Figure 1.5. Simulated values for (i, q˜) and (i, cf ) , with only temporary shocks. Regression results After considering these two extreme cases we introduce both persistent and temporary shocks and run multivariate investment regressions. In particular, we vary the fraction of the variance generated by the persistent shock to the total variance of productivity, V ar(x)/V ar(a) and study the eﬀect on the coeﬃcients on q˜ and cash flow.17 We simulate our model for 200 periods. We generate 500 sample series and use these series to obtain average coeﬃcients and standard deviations.18 Namely, for each simulated series we run the standard investment regression µ

I K

¶

= a0 + a1 q˜t + a2 cft + et

t

Existing empirical estimates of this regression are mostly based on panel data, while our model’s immediate implications are in terms of time series. However, it is not diﬃcult to 17

In our computation we look at a log-linear approximation of K. Therefore, only the ratio between the two shocks matters for our regression coeﬃcients. 18 At a later point we will calculate standard errors corresponding to the empirical regressions.

28

extend our model to a version with multiple sectors. If we assume that productivity Ait is the same within a sector, and that labor and old capital are immobile across sectors, the panel implications of our model are identical to the time series implications. One can rewrite the model introducing a sector-specific wage rate wit and a sector-specific price of old capital qito , and all the results obtained above carry over at the sector level. The role of immobile labor is to generate decreasing returns at the sector level without introducing decreasing returns at the firm level. The advantage of having “external” decreasing returns is twofold. First, absent financial frictions, Hayashi’s theorem applies, and so we can study the role of financial frictions separately from the role of decreasing returns. The role of decreasing returns in generating deviations from standard q theory has been investigated in Cooper and Ejarque (2001) and Abel and Eberly (2002), so it is useful at this stage to study the role of financial constraints separately. Secondly, the individual problem of the entrepreneurs remains linear, which simplifies the analysis of the optimal financial contract. In section 1.5 we consider the polar opposite case where labor and capital are fully mobile across sectors, so that the wage rate and the price of old capital goods are equalized across sectors. As a reference point, it is useful to look at the coeﬃcients obtained in Gilchrist and Himmelberg (1995). Their panel data results are q˜ (s.e.)

cf (s.e.)

0.033 (0.016)

0.242 (0.038)

Table 1.1. GH (1995) Empirical multivariate investment regressions. The serial correlation of the investment rate (below denoted “s.c. I/K”) is 0.4 in the Compustat sample that Gilchrist and Himmelberg (1995) use. Multivariate regression results for the simulated model is presented in Table 1.2, for a range of relative variance parameters.

29

V ar(x)/V ar(a) q˜ (s.d.)

cf (s.d.)

s.c. I/K

R2

1

1.50 (0.00)

-1.70 (0.00)

0.86

1.00

0.8

0.33 (0.07)

0.25 (0.17)

0.75

0.70

0.6

0.14 (0.06)

0.54 (0.04)

0.43

0.77

0.4

0.08 (0.08)

0.59 (0.01)

0.14

0.92

0.2

-0.02 (0.07)

0.59 (0.00)

0.01

0.98

0

-0.12 (0.00)

0.59 (0.00)

-0.01

1.00

Table 1.2. Multivariate regression results. It should be no surprise that we get a R2 of 1.0 in a model with only one type of shock (i.e. for relative variance of 1 or 0) and no measurement error or unobserved heterogeneity. The valid way of comparing our simulated regression results to empirical studies is to look at the relative size of the regression coeﬃcients, as the coeﬃcients from the model will always be larger than their empirical counterparts for the same reason that R2 is higher. The size of the coeﬃcients in the multivariate regressions are also aﬀected by the high collinearity in the extreme cases (relative variance of 1 or 0). Our fourth case, for V ar(x)/V ar(a) = 0.4, comes reasonably close to replicating the relative size of the two coeﬃcients. We also run univariate regressions of the investment rate on observed q˜ and cash flow respectively, to see how much each variable can explain of the variation in investment rates. The results are reported in Table 1.3 and Figure 1.6.

30

V ar(x)/V ar(a) univar. q˜ (s.d.) R2 of q˜ univar. cf (s.d.) R2 of cf 1

0.46 (0.03)

0.77

0.62 (0.08)

0.56

0.8

0.47 (0.06)

0.68

0.66 (0.12)

0.61

0.6

0.44 (0.06)

0.36

0.61 (0.05)

0.76

0.4

0.33 (0.09)

0.08

0.60 (0.02)

0.92

0.2

-0.04 (0.10)

0.00

0.59 (0.00)

0.98

0

-0.43 (0.22)

0.01

0.59 (0.00)

1.00

Table 1.3. Univariate regression results. As we increase the relative variance of the persistent shock, the explanatory power of observed q˜ goes from 0 to 0.77, while the explanatory value of cash flow decrease from 1 to 0.56. These results are most clear in Figure 1.6 where we also plot the explanatory power of the multivariate regression. 1.00

R-square

0.80 R² of q

0.60

R² of cf 0.40

R² multiv.

0.20 0.00 0

0.2

0.4

0.6

0.8

1

Var(x)/Var(a)

Figure 1.6. Univariate R2 of cf and q˜, respectively, and the R2 of the multivariate regression, as a function of the persistent shock’s relative contribution to the variance of productivity.

31

1.5 1.5.1

Extensions Mobile labor and capital

Consider a version of our model where capital and labor is fully mobile between sectors. Also assume firm-specific productivity shocks and no aggregate uncertainty. The constant aggregate technology implies that aggregate q is constant and equal to 1, and q o is constant and equal to (1 − δ). The state space is (X, K) and there is a stationary distribution of firms in this

space.19 The full equilibrium is not trivial, but we can derive what we need for the investment regression because the relevant relationships are linear. Start by deriving the static choice of labor for each firm from the expression for gross profits Rit Kit which is a sum of flow profits and the value of undepreciated capital: − wLit + (1 − δ)Kit } Rit Kit = max{Ait Kitα L1−α it Lit

The first order condition for labor yields the optimal choice of labor/capital ratio for each firm:20 (1 − α) Ait Kitα L−α = w it ¶1/α µ Ait Lit = (1 − α) Kit w

(1.10)

Note that the labor/capital ratio will vary positively with Ait across firms. We can rewrite the expression for gross profits as Rit Kit

µ

¶1−α ¶ µ Lit Lit Kit + (1 − δ)Kit = = Ait Kit −w Kit Kit " µ ¶1−α ¶# µ Lit Lit Kit + (1 − δ)Kit −w = Ait Kit Kit

19

Recall that x denotes the persistent part of the productivity process. The wage is determined by the aggregate capital/labor ratio. To solve for the aggregate capital stock we need to solve for the joint distribution of (X, N ). For now we will use the capital stock of the earlier exercise. Regression coeﬃcients are not very sensitive to the size of the aggregate capital stock. 20

32

Plugging in for

Lit Kit

from (1.10) we note that flow profits are simply a function of Ait times

Kit . The above expression simplifies to 1/α

Rit Kit = bAit Kit + (1 − δ)Kit

(1.11)

where b = α(1 − α)1/α−1 w1−1/α . b is a constant for the total eﬀect of productivity on R, taking into consideration the indirect eﬀect through

Lit . Kit

We obtain the following expression

for each firm’s return to capital Rit : 1/α

Rit = bAit + 1 − δ We note that Rit is completely independent of scale. Because of the mobile labor (and only idiosyncratic shocks) there are no general equilibrium eﬀects that create decreasing returns to a factor (as opposed to in the model with immobile labor presented earlier). From (1.11) we see that 1/α

cfit = bAit

(1.12)

Because there are no capital gains (qt = 1 ∀t) the diﬀerence between cash flow and Rit is just the constant (1 − δ). The expression for firm level observed q˜it is q˜it ≡

Vit Kit+1 βEt {Rit+1 } Kit+1 = = βEt {Rit+1 } Kit+1 Kit+1

(1.13)

i.e. simply discounted expected next period return to capital. Finally, we derive the expression for (net) investment using equation (1.8) for surviving firms. The absence of firm-level adjustment costs makes it optimal for each firm’s capital stock

33

to immediately adjust fully to any firm-level productivity shock, given the collateral constraint. Iit = Kit+1 − Kit = (1 − θ) Rit 1 Nit−1 − Kit = = 1 − βθEt {Rit+1 } 1 − βθEt−1 [Rit ] (1 − θ) Rit = Kit − Kit 1 − βθEt [Rit+1 ] Then the investment rate is Kit+1 − Kit Iit = = Kit Kit (1 − θ) Rit = −1 1 − βθEt [Rit+1 ]

(1.14)

We end up with three closed form equations, (1.12)-(1.14), for the variables in the investment regression. Regression results This version of the model is well suited for cross-sectional regressions, without any need for re-interpretation. Following the empirical literature we run21 µ

I K

¶

= a0 + a1 qit + a2 cfit + vi + eit

it

From equations (1.12)-(1.14) we can directly see that in the absence of temporary shocks, both q˜it and cfit are fully correlated with investment. With only temporary shocks, q˜it is constant and only cfit is (fully) correlated with investment. It follows that multivariate R2 will be 1 and the univariate R2 of cf will be close to 1 for all types of shocks. The univariate R2 of q˜ will go from 0 to 1 as the relative contribution of the persistent shocks increases, as illustrated in Figure 1.7. 21

This is identical to the panel data literature, except that there one must add a time dummy to eliminate aggregate variations. We run the regression in terms of de-meaned levels (which means that there is no need to include a firm-specific eﬀect vi and that we can exclude the intercept ao ).

34

1 0.8 R² of q R-square

0.6

R² of cf

0.4 0.2 0 0

0.2

0.4 0.6 Var(x)/Var(a)

0.8

1

Figure 1.7. Univariate R2 of cf and q˜, respectively, as a function of the persistent shock’s relative contribution to the variance of productivity.

The multivariate coeﬃcients (for the intermediate range) are pinned down by (1.12)-(1.14). We know that the collinearity of q˜ and cf is high for V ar(x)/V ar(a) close to 1, and this will aﬀect the multivariate regression. The results are presented in Table 1.4.

V ar(x)/V ar(a)

q˜

cf

R2

1

-1.24

2.51

1.00

0.8

0.47

1.02

1.00

0.6

0.47

1.02

1.00

0.4

0.47

1.02

1.00

0.2

0.47

1.01

1.00

0

0

1.01

1.00

Table 1.4. Multivariate regression results for cross-sectional model with mobile labor. This version of our model, with mobile factors, yields a regression coeﬃcients for q˜ that is too large relative to the cf coeﬃcient compared to the the empirical estimates. Furthermore, 35

the level of both coeﬃcients is extremely high and the explanatory power of cash flow is too high. This is a direct result of the linear relationships between the relevant variables. To make this version of the model fit the empirical regression coeﬃcients, we would need to artificially introduce measurement error or unobserved shocks.

1.5.2

Occasionally binding constraints

So far we have assumed that shocks are small enough that Proposition 2 applies and the financial constraint is always binding. This assumption is a useful simplification for two reasons. First, it reduces the state space for a recursive equilibrium to Kt , while in general the state space is given by both Nt and Kt . Second, the optimal financial contracts is simply given by Dt+1 = θRt+1 Kt+1 while in the general case, the optimal financial contract is described by a function of the type D (st+1 , Nt , Kt ) which can specify diﬀerent payments for each realization of the exogenous state st+1 next period. As a first step in the analysis of the general case, we consider here the case of an economy that is hit by a single temporary shock at time τ . After time τ , the productivity level is deterministic and equal to A. If the temporary shock is suﬃciently large, the firms enter a path in which the financial constraint is not binding for the first T − τ periods, and is binding again afterwards. In particular, condition (2.2) holds as an equality for t, τ ≤ t ≤ T, and we have φt = (1 − γ) φt+1 + γ Condition (1.6) tells us that in this case investment is determined by the condition qt = βRt+1

36

and the evolution of entrepreneurial wealth is given by Nt+1 =

1−γ Nt + γwt LE β

Since the rate of return on entrepreneurial wealth is lower than in steady state, entrepreneurial wealth declines over time up to the point where the financial constraint is binding again. The dynamics of investment in this case are illustrated in Figure 1.8 for diﬀerent values of the temporary shock. In the first panel of Figure 1.8 we report the dynamics of entrepreneurial wealth N, in percentage deviations from the steady state. In the second panel, we report the dynamics of the investment rate. The figure shows that the relation between cash-flow shocks and investment is non-linear and that the propagation depends on the size of the shocks. For small shocks the firm uses all the extra cash flow to invest in physical capital, so the eﬀect at impact (normalized by the size of the shock) is large, but it dies out quickly. For large shocks the firm instead invests only a fraction of the extra cash flow in physical capital, and invests the rest at the risk free rate. The firm eﬀectively is accumulating cash reserves to be used for investment in the following periods. The impact eﬀect is smaller (when normalized by the size of the shock) but the response of investment is more persistent. These dynamics are driven by the interaction of the financial constraint and the adjustment cost. With no financial constraint the temporary shock would have no eﬀect on investment, and with no adjustment cost the temporary shock would only have temporary eﬀects on investment. The interest in this result lays in the fact that with occasionally binding constraints, we can reduce the eﬀect of cash flow on investment and we can increase the serial correlation of the investment rate after a temporary shock. If one goes back to the simulations reported in Table 1.2 and compares them with the Gilchrist and Himmelberg (1995) coeﬃcients reported in Table 1.1 one can see that both eﬀects help match the empirical evidence for low levels of V ar (x) /V ar(a).

37

0.5 0.4

n

0.3 0.2 0.1 0 2

4

6

8

10

2

4

6

8

10

12

14

16

18

20

12

14

16

18

20

0.06 0.04 i

0.02 0 -0.02 -0.04 t

Figure 1.8. Impulse response functions of entrepreneurs’ wealth N (top panel) and investment rate I (bottom panel) to temporary shocks of various sizes.

1.6

Conclusion

In this paper we have considered a framework for thinking about the eﬀect of financial frictions on asset prices and Tobin’s q. The main conclusion is that in the presence of financial frictions q may reflect some of the future rents that will go to the insider. Since the insider’s shadow discount factor is diﬀerent from the market discount factor, these future rents are “mispriced” and the value of the firm appears larger than the value of installed capital. Then, observed q is larger than one. The next step is to explain whether the variation in the value of these rents can help us explain the empirical lack of correlation between investment and q. In this paper we have proposed a simple model with temporary and persistent shocks and have shown that, if temporary shocks are large enough, we can roughly replicate the correlations observed in the empirical data. This is due to the fact that temporary shocks generate a negative correlation between

38

investment and future rents. However, we have not yet explored the various configurations of shocks that can determine changes in future rents with small or negative eﬀects on current investment. For example, news shocks that aﬀect future profitability without aﬀecting current profits will have a large eﬀect on q, by increasing future rents, and a small eﬀect on investment. An open question is whether a realistic process for productivity at the firm level can help us explain the observed correlation between q and in investment. This seems to be a problem common to our approach and to the approach based on market power and decreasing returns at the firm level. For example, Cooper and Ejarque (2001) use an AR(1) process for productivity with ρ = 0.11. Moreover, since they only use this type of “temporary” shocks, they obtain a negative unconditional correlation between investment and q.22 Furthermore, they recognize that due to the low persistence of the technology shock, their model has a hard time replicating the empirical autocorrelation of investment rates. It is interesting to notice that in our framework we would encounter similar problems if we had only one type of shock. In the current paper, we partially solve the problem by adopting a mixture of temporary and persistent shocks. However, the crucial question is whether the amount of temporary volatility needed to explain the observed relation between q and investment in models with financial frictions (or market power) is in a realistic range. One potential extension could be to include decreasing returns to scale. In the present paper we assumed constant returns to scale to clarify the role of the financial constraint, but to quantitatively explore the eﬀects of decreasing returns to scale and financial constraints, respectively, it would be interesting to put both mechanisms in the model. A second possible extension is to use concave preferences for the consumers and let the interest rate be endogenously time varying. To match the existing literature, we geared the model to cross-sectional diﬀerences between firms. On the other hand, from a time-series perspective, the interaction between the risk-free rate and q might be worth exploring. 22

We obtained this result when replicating their simulations. A similar result arise in our model if only a temporary shock is present.

39

Chapter 2 Temporary and Persistent Shocks in Tobin’s q Theory - An Empirical Assessment 2.1

Introduction

The aim of this paper is to explore whether the relationship between productivity, Tobin’s q and investment is diﬀerent when a firm is hit by a temporary productivity shock than when hit by a persistent productivity shock. The main reason we study this conditional relationship is to test the model of Lorenzoni and Walentin (2005) (hereafter LW). LW constructed a model of investment with a collateral constraint on firms’ borrowing where Tobin’s q theory holds conditional on persistent productivity shocks. A second motivation for studying this relationship is as a humble beginning of a broader program to document and explain empirical regularities in firm dynamics. The key part of the LW model is a collateral constraint that implies that a positive temporary (i.i.d.) shock to productivity will lower Tobin’s q and at the same time increase investment of financially constrained firms, generating a negative conditional relationship between Tobin’s q and investment. It is this mechanism that lies behind one key result of LW - the matching of 40

the investment regression coeﬃcients on Tobin’s q and cash flow that the empirical literature reports (Gilchrist and Himmelberg (1995) and others) in a micro-founded dynamic stochastic general equilibrium (DSGE) model. In other words, LW attribute the empirical violations of q theory that have been widely documented in the literature to the combination of binding collateral constraints and temporary productivity shocks. To empirically test the LW model we use three complementary approaches. In the first approach we simply sort industry sectors by the degree of persistence to productivity that they are characterized by. We order them into groups according to persistence and for each group we run the standard investment regression. In this way we test whether there is a (positive) relationship between the persistence of shocks and the performance of Tobin’s q theory. Second, we use a panel dataset of firms and divide the firm-year observations into four groups according to the sign of the comovement between q and investment, and the sign of the change of investment. The LW model implies that if a persistent shock hits, q and investment will move together, and if a temporary shock hits they will move in opposite directions. We test this implication by studying whether comovement of q and investment indicates that a persistent shock has hit the firm. Third, we again run the investment regression, but divide the observations into sample split groups according to their productivity growth. The idea behind this method is to let extreme values of medium term productivity growth proxy for a persistent shock. By estimating the investment regression on this sample split we get a direct test of whether q theory does better conditional on persistent shocks. In a broad sense, the present paper is part of a large literature that deals with firms’ capital investment, Tobin’s q and financial constraints. On the empirical side the seminal paper is Fazzari et al. (1988). For a survey see Hubbard (1998). In a more narrow sense, the LW model that we test in this paper is most closely related to Gomes (2001), Cooper and Ejarque (2003) and Abel and Eberly (2005). The LW model share the characteristic with all these models that it tries to clarify the empirical results from investment regressions on Tobin’s q by setting 41

up a general equilibrium model, with or without financial frictions, and then run investment regressions on the simulated output from the model. The next section of the paper contains the LW model to motivate and focus our interest in studying the potentially diﬀerent eﬀects of temporary and persistent shocks. Section 2.2.6 is of particular interest as it describes the implication of the model that we test. Section 2.3 describes the data used and section 2.4 contain the empirical work. Section 2.5 concludes.

2.2

Model

The aim of this section is to describe the LW model, with an emphasis on how it generates a wedge between the q that we observe in financial markets, “observed q” (denoted q˜), and the shadow price that determines optimal investment, “shadow q” (denoted q). We also show how the dynamics of this wedge depends on the type of productivity shock, i.e. temporary or persistent. The LW model is a DSGE model of investment with constant returns to scale production, convex adjustment costs of investment and two groups of agents: consumers and entrepreneurs. Each group of agents is composed of a continuum with unit mass. The key feature of the model is a collateral constraint on entrepreneurs’ borrowing. The presence of both persistent and temporary shocks to productivity interacts with the collateral constraint, and this is the only aspect that makes the model diﬀerent from traditional Tobin’s q theory.

2.2.1

Preferences

Consumers are infinitely lived and risk-neutral. Their preferences are represented by: E

∞ X

β t Ct

t=0

Further, consumers have a constant endowment of labor LC each period.

42

Entrepreneurs are also risk-neutral and have the same subjective discount factor β, but a stochastic life span with constant probability of death γ. Each period a fraction γ of entrepreneurs learn that this will be their last period. They liquidate all their capital, pay oﬀ their debts, and consume the residual.1 The preferences of entrepreneurs alive at time t are described by the utility function Et

∞ X j=0

¡ ¢ e d β j (1 − γ)j (1 − γ) Ct+j + γCt+j

where Cte is consumption in any period before the last, and Ctd is consumption in the last period before death.

2.2.2

Technology

Entrepreneur i accumulates capital, hires labor and operates the constant returns to scale technology described by the Cobb-Douglas production function At F (Kit , Lit ). To install new capital entrepreneurs face the convex adjustment cost function G (I, K). The law of motion for capital is: Kit+1 = (1 − δ) Kito + Iit where Kito denotes “used” capital and Iit is investment. The only source of randomness in the model is the level of technology At = eat where at follows the process at = xt + η t xt = ρxt−1 +

t

Both η t and εt are Gaussian i.i.d. shocks, so that η t represents a temporary shock while xt captures the persistent part of the productivity process. 1

The fact that entrepreneurs die does not aﬀect their discounting as they get a signal of death and have time to consume before dying. This aspect is diﬀerent from some earlier models of financially constrained entrepreneurs.

43

2.2.3

Collateral constraint

There is a full menu of one period state contingent securities. Denote a node (s0 , ..., st ) by st . At node st the entrepreneur sells state contingent promises Di (st+1 |st ) (denoted by Dit+1 ) to

be paid next period, if node (st , st+1 ) is reached.

The only incompleteness in the financial markets comes from limited enforcement which creates the collateral constraint. The motivation is as follows: Each entrepreneur has full control over his firm’s assets. At the beginning of each period the entrepreneur can choose to divert part or all of the capital stock. The only recourse creditors have against such behavior is liquidation of the firm. For each unit of diverted capital the entrepreneur is able to capture (1 − θ) units. After diversion the firm is liquidated, the entrepreneur keeps (1 − θ) Kit+1 and

can start a new firm.2 Therefore, to give incentives that prevent diversion, the value of the

claims held by the insider must be at least (1 − θ) times the value of the firm. Accordingly, entrepreneurs can credibly only commit to pay back up to a fraction θ of gross profits. In equilibrium there is no diversion and no liquidation. The gross profits of a firm are Rt Kit = max {At F (Kit , Lit ) − wt Lit + qt Kit (1 − δ)} Lit

where wt is the wage rate and qt the price of capital. Because of the assumption of constant returns to scale Rt is identical for all entrepreneurs. The collateral constraint implies Dit+1 ≤ θRt+1 Kit+1

(2.1)

Let m (st+1 |st ) (denoted by mt+1 ) be the consumer’s state contingent stochastic discount factor and Nit the net wealth the entrepreneur carried over from the previous period. The resulting 2

For simplicity, we assume that (1 − θ) Kit+1 can still be used for production immediately after diversion.

44

upper bound on the capital of entrepreneur i is: qt Kit ≤ Nit + Et [mt+1 Dit+1 ] This inequality implies that an entrepreneur can not use a capital stock larger than the sum of his net wealth and the discounted value of his next period (credible) promises, i.e. what he can finance externally. We note3 that the shadow price of new capital qt satisfies qt = GI

µ

¶ It ,1 . Kt

This is the standard relation between marginal q and investment in a model with convex adjustment costs. This relation still holds in our model. Therefore, deviations from q theory must be due to the diﬀerence between this shadow q and observed q˜. We will see in section 2.2.6 below what the dynamics of the wedge between these are.

2.2.4

Entrepreneur’s problem

The entrepreneur’s problem can be described in recursive terms using the value function Vt (Nit ) that denotes the expected utility of a surviving entrepreneur with wealth Nit at the beginning of period t. The Bellman equation characterizing Vt is Vt (Nit ) = Cite

max e

{Dit+1 },Cit ,Kit+1

Cite + βEt [γNit+1 + (1 − γ) Vt+1 (Nit+1 )]

+ qt Kit+1 ≤ Nit + Et [mt+1 Dit+1 ] Dit+1 ≤ θRt+1 Kit+1 Nit+1 = Rt+1 Kit+1 − Dit+1

3

See Lorenzoni and Walentin (2005) for the derivation.

45

Given the linearity of the problem, the value function will have a linear form Vt (Nit ) = φt Nit where φt depends on current and future prices that are taken as given by the entrepreneur. The optimal financial contract is characterized by the first order conditions ¡ ¡ ¢ ¡ ¢ ¢ − β γ + (1 − γ) φt+1 πKit+1 + λ st mt+1 πKit+1 − µ st+1 |st = 0 ¤ £¡ ¢ βEt γ + (1 − γ) φt+1 (Rt+1 Kit+1 − Dit+1 ) − ¡ ¢ λ st (qt Kit+1 − Et [mt+1 Dit+1 ]) = 0 where λ (st ) is the Lagrange multiplier on the budget constraint and µ (st+1 |st ) is the Lagrange multiplier on the collateral constraint in state st+1 . The envelope condition gives us Vt0 (Nit ) = φt = λt . Consider a node st and an entrepreneur’s decision regarding his financial liabilities in the subsequent node (st , st+1 ). The entrepreneur will compare the marginal value of a dollar today, ¡ ¢ φt , to the marginal value of a dollar tomorrow in state st+1 , given by β γ + (1 − γ) φt+1 . If the following inequality holds for node (st , st+1 )

¢ ¡ β γ + (1 − γ) φt+1 < φt mt+1

(2.2)

then it is optimal to borrow as much as possible in state st+1 and use the proceeds to invest today. In this case µ (st+1 |st ) > 0 and the optimal financial contract is given by Dit+1 = θRt+1 Kit+1 . In an equilibrium with mt = β it is possible to prove that (2.2) implies φt > 1 and Cite = 0. Then Kit+1 is given by Kit+1 =

1 Nit qt − θEt [mt+1 Rt+1 ] 46

(2.3)

for all surviving entrepreneurs. Aggregating (2.3) across entrepreneurs, and combining with the law of motion for Nt we get the law of motion for the only endogenous state variable, Kt . To preserve space we will not here describe the aggregation of entrepreneurs, define the full equilibrium or lay out the full solution of the model, but instead refer the reader to Lorenzoni and Walentin (2005). It suﬃces to mention that for a large subset of the parameter space there exists a stochastic steady state where the collateral constraint is always binding provided that the size of shocks are bounded. Existing empirical estimates of this regression are mostly based on panel data, while the LW model’s immediate implications are in terms of time series. However, it is not diﬃcult to extend the model to a version with multiple sectors. If we assume that productivity Ait is the same within a sector, and that labor and old capital are immobile across sectors, the panel implications of our model are identical to the time series implications. One can rewrite the model introducing a sector-specific wage rate wit and a sector-specific price of capital qit , and all the results obtained above carry over to the sector level. This is the path we pursue when we test the model empirically below.

2.2.5

The tightness of the collateral constraint

The tightness of the financial constraint corresponds to the marginal value of wealth, measured by the Lagrange multiplier λ (st ) on the entrepreneur’s budget constraint. The constraint is tight when the distance is large between the first best capital stock (at which the discounted gross return to capital equals 1) and the actual capital stock that the entrepreneur can fund. Note that there is a scarce resource in this economy — entrepreneurial funds. The scarcity generates quasi-rents which are priced into the market value of each firm, creating the wedge between shadow q and observed q˜.4 The tighter the financial constraint, the larger are the quasi-rents and the wedge between q and q˜. 4

Further, the quasi-rents are “mispriced” using the discount factor of the consumers, which is diﬀerent from the entrepreneur’s discount factor.

47

2.2.6

Dynamics of the wedge, and the resulting correlation between q˜ and investment

We are now in a position where we can describe the key implication of the model that is tested in the present paper. The eﬀects of a positive persistent productivity shock are the following: The increased future profitability increases the level of first best capital stock. At the same time, the entrepreneur’s resources increase because he receives extra cash flow today and can increase his leverage, thanks to the increase in the pledgeable next period gross profits. The first eﬀect dominates, given the high persistence of the shock, and this implies that the gap between the first best capital stock and the feasible capital stock increases. The larger gap corresponds to a tighter financial constraint and a higher observed q˜. At the same time, investment, denoted by i, increases and we get a positive contemporaneous relationship between investment and q˜. This is the standard result in Tobin’s q theory. Accordingly, in a simulation of the LW model with only persistent shocks Corr(˜ q, i) > 0, and q˜ is a suﬃcient statistic for investment (see Lorenzoni and Walentin (2005) for details on regressions on simulated data). The above dynamics are illustrated as impulse response functions in the first column of Figure 2.1.

48

Persistent shock ε

1

Temporary shock η

1

a

0.8 0.6

0.5

0.4 0.2

0

2

4

6

8

0

10

0.2 0.15

0.1

0.1

0.05

i

0

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

0.15

0.05

0

0

-0.05

0

2

4

6

8

10

0 -3

0.4

-5

obs. q

0.3

x 10

-6

0.2 -7

0.1 0

0

2

4

6

8

-8

10

0

Figure 2.1. Impulse response functions of (by row) productivity, investment and observed q˜ to persistent and temporary technology shocks.

The eﬀects of a positive temporary (i.i.d.) productivity shock are diﬀerent. A temporary shock can be viewed as a pure wealth shock to an entrepreneur, as future profitability is unchanged. The direct result of the shock is that the entrepreneur becomes less financially constrained, increases his investment and moves closer to the (unchanged) first best capital stock. Accordingly, the gap between the first best capital stock and the feasible capital stock shrinks and observed q˜ falls. A negative contemporaneous relationship between investment and observed q˜ therefore holds. In a simulation with only temporary shocks Corr(˜ q , i) < 0. Furthermore, in this case q˜ has almost no explanatory value for investment which instead is fully explained by cash flow. The second column of Figure 2.1 illustrates the dynamics.

2.3

Data

We use two diﬀerent datasets for productivity, one sector-level data set, and one firm-level dataset. All other variables are always taken from the firm-level dataset.

49

2.3.1

Compustat

For firm-level data we use the Compustat dataset of firms. Compustat covers 1950-2003 annually for all stock market listed US firms. The number of firms are growing over time, and to keep the composition of firms reasonably stable it is common to restrict the time period to 1970 and onwards, and we follow this convention. For our main results we restrict our sample to firms in the manufacturing sector, to follow the great majority of the empirical work on Tobin’s q. We further limit the dataset by requiring 15 years of observations to include a firm in the final dataset. To reduce the impact of outliers we exclude the top and bottom 1% observations for the variables of interest. All variables are converted from nominal to real values using the consumer price index.

2.3.2

NBER Manufacturing Productivity Database

To complement the firm-level data we use a sector dataset with total factor productivity (TFP) properly measured called ’NBER Manufacturing Productivity Database’ (Bartelsman and Gray (1996)) (hereafter NBER-CES) which contains TFP measured on the 4-digit SIC sector level for 459 manufacturing sectors for 1958—1996.5 We only use the time period from 1970 onwards, to be consistent with the time period for which we have good data on q˜ and investment. By matching 4-digit SIC sectors we combine the TFP measure from the NBER-CES dataset with variables from Compustat, either on a firm-level or by aggregating firm values into sector values. We exclude sectors where we do not have 15 years of observations from both datasets. The resulting dataset is an almost balanced panel of 89 3-digit SIC sectors, or 131 4-digit SIC sectors, 1970-1996.

2.3.3

Variables

Observed q, denoted q˜t , is the the end of year t ratio

market value of firm it , book value of capitalit

where book value is the

accounting value of total assets of the firm. The maintained (but strong) assumption is that 5

We use the 5 factor variable, named "tfp5".

50

book value is a good proxy for the replacement cost of capital. iit =

investmentit P P Eit−1

denotes the

gross investment/capital ratio during year t. P P Eit−1 is “Property, Plant and Equipment” at the end of the previous year. Reliable TFP measurements on the firm level are not available. To proxy the productivity Ait (or, ideally profitability) of a firm we use several alternative variables. We follow the literature for Compustat data and use Sales per Employee as our measure of (labor) productivity, denoted by Ait . In particular, we use ∆k+1 ait+k ≡ log(Salesit+k /# of Employeesit+k ) − log(Salesit−1 /# of Employeesit−1 ) as our measure of productivity growth between year t − 1 and year t + k. We also use a similar measure for sales growth, and denote this by s. Our third alternative proxy is Sales/PPE (referred to as Sales/Capital) which is used as a measure of capital productivity. The problem with all these proxies for productivity is that none of them is truly exogenous. In interpreting the results of the two last approaches used to test the LW model we must therefore understand how the factor input choices of the firm will aﬀect the productivity measure over time. The point here is that for a profit maximizing firm, labor productivity or capital productivity is not going to stay above the average level forever, even following a permanent shock, as factor inputs will be adjusted over time to eliminate any abnormal returns. We use the standard Compustat definition for cash flow, cfit =

CFit , P P Eit

where CF is defined

as “profits before extraordinary items+depreciation and amortization”. Table 2.1 contains the descriptive statistics for the final firm-level dataset of 1417 firms for the years 1972-2003 totalling 31.267 firm-year observations.6 6 Because of the forward looking nature of ∆5 ait+4 and ∆5 sit+4 , for these variables we only have 902 firms for 1972-1999, totalling 20.436 firm-year observations.

51

Variable

mean

std.dev. min

max

∆5 ait+4

0.0597 0.2531

-1.0301 1.3207

∆5 sit+4

0.1319 0.4557

-1.6360 2.1382

At

102.7

65.31

0.542

601.1

Sales/Cap 6.208

5.533

.0018

87.97

q˜

1.543

1.114

0.532

15.446

i

0.273

0.264

0.001

3.018

cf

0.332

0.965

-27.038 5.604

Table 2.1. Descriptive statistics for Compustat data. An important point to note in the descriptive statistics (which is not shown in Table 2.1) is that close to half of the firm-year observations have q˜ and i that move in diﬀerent directions.7 This is consistent with LW, but from a traditional Tobin’s q theory perspective it must be interpreted as noise as q theory predicts that q and i comove perfectly.

2.4 2.4.1

Empirical work Estimation method for persistence of productivity

We use a panel of productivity observations, per sector or firm. We estimate the degree of persistence of productivity for each sector. We are only interested in the stochastic part, so we first detrend productivity (at the sector level) using a quadratic time trend.8 We use three alternative measures of persistence. For the first measure we estimate an AR(1) process using Arellano and Bond’s method of dynamic panel data estimation. We denote the estimated autoregressive parameter by ρ. For the second measure we estimate the fraction 7

This fact is not caused by investment decision lags: the fraction stays approximately the same if we instead look at the degree of comovement using one-year ahead investment. 8 We thereby implicitly assume that the deterministic part of productivity (at this level) is trend-stationary.

52

of variance in productivity that come from persistent shocks, as opposed to temporary (i.i.d.) shocks. We denote this fraction by

σ2pers . σ2tot

The method exploits the panel structure of the data.

The details are presented in the Appendix. Note that in the presence of i.i.d. measurement error

σ 2pers σ 2tot

will be biased downwards. Our third measure is a non-parametric measure from

Cochrane (1988). It involves calculating σ 2C,k =

V ar(xt − xt−k ) k

for each time-series {xt } for diﬀerent lag lengths k. The fraction

σ 2C,k σ2C,1

then denotes how persistent

the process is. For a unit root process this fraction is constant over k and equal to 1, and the less persistent the process is, the faster does the fraction converge towards 0. We report the result of this measure for a lag length of 5 years. Each of these three measures have advantages. ρ is easy to interpret and can be estimated tightly.

σ2pers σ2tot

is closest to the key parameter of the LW model, and

σ 2C,k σ2C,1

does not impose a

functional form for the shock process. We therefore use them all.

2.4.2

Estimation of model parameters

Our first exercise is related to the calibration of the LW model. We estimate

σ2pers , σ2tot

the fraction

of the variance of productivity that comes from persistent shocks, as opposed to temporary shocks. To match the coeﬃcients on q˜ and cash-flow that the empirical literature reports, the LW model needs a substantial amount of temporary shocks, corresponding to

σ2pers σ2tot

= 0.4. We

also report the estimated ρ. Both parameters are estimated on detrended 4-digit SIC sector productivity. Table 2.2 reports the estimates using NBER-CES sector data.

53

Parameter Estimate (s.e.) ρ

.850 (.026)

σ2pers σ2tot

.640 (n/a)

Table 2.2. Persistence estimates on the 4-digit SIC sector level using NBER-CES TFP. n=10.085, 417 sectors. The standard errors for ρ are robust. We note that there is a lot of temporary volatility in sector productivity, but not as much as LW model requires to exactly match its target coeﬃcients. Furthermore, the estimated ρ for sector productivity is substantially lower than the ρ for the aggregate economy reported in the literature. One problem in the mapping from the TFP persistence estimate to the model remain: Potentially there are other shocks than technology that aﬀect the profitability of a sector or a firm. In principle these shocks, which arguably are less persistent, should also be used in the estimation of

σ 2pers , σ2tot

as the the LW model only contains one type of shock. We therefore view

the above estimate of

σ2pers σ2tot

as an upper bound on the parameter that should be used for the

LW model.

2.4.3

Grouping by sector persistence

Method In our first approach to test the LW model, we sort the sectors into 5 groups in ascending order according to persistence, so that the least persistent sectors (or firms) are placed in group 1, and the most persistent in group 5. We then run the standard investment regression from Fazzari et al. (1988), separately for each group, and compare the regression coeﬃcients between the groups.

54

The standard investment regression is

iit = a0 + a1 q˜it−1 + a2 cfit + ui + vt + eit

(R0)

i.e. investment during year t is regressed on the end of year t-1 q value and the cash flow (cf ) for year t. ui denotes a firm fixed eﬀect, and vt is a year dummy to eliminate covariation due to aggregate eﬀects. The LW model have direct implications for what happens when a persistent or a temporary (i.i.d.) shock hits a firm. As shown in section 2.2.6 this leads to clear predictions for a sector with only persistent shocks, or a sector with only temporary shocks, respectively. We estimate the persistence of the productivity process by sector. These estimates are based on noisy measures of productivity and are therefore quite inexact. Furthermore, as mentioned above, the LW model’s implications are for the extreme cases. We therefore limit our attention to comparing the coeﬃcients between the extreme groups. Recall that the model predicts that q theory holds conditional on (only) persistent shocks. This implies that compared to group 1, the coeﬃcient on q˜, a1 , will be higher for the more persistent group, group 5. Analogously, the coeﬃcient on cf , a2 , is predicted to be lower for group 5 than for group 1. Persistence measures for sector level data We divide the sample per 3-digit SIC sector. For each 3-digit sector we estimate persistence on a panel of 4-digit SIC TFP from the NBER-CES. The results for the persistence measures are presented in Table 2.3.

55

Parameter Mean Cross-sectoral standard deviation Std.error ρ

.717

.141

.060

σ2C,5 σ2C,1

.661

.290

.335

σ2pers σ2tot

.501

.180

n/a

Table 2.3. Persistence measures on the 3-digit SIC sector level using NBER-CES TFP. n=10.085, 417 4-digit sectors, 89 3-digit sectors. The standard errors (s.e.) for σ 2C,5 /σ 2C,1 are Bartlett s.e. The s.e. for ρ are robust. Is the diﬀerence between sectors large enough to be useful in testing the eﬀects of diﬀerent degrees of persistence? We perform a pairwise comparison of each of the estimated ρˆ0i s by checking if the upper bound of the confidence interval of ρˆi is lower than the lower bound of the confidence interval for ρˆj . We use a 95% confidence level. With this method, the lowest ρˆi is significantly diﬀerent from 53 of the 88 other estimates. Out of 3916 pairwise comparisons, 910 of the ρˆi are significantly diﬀerent from each other. Table 2.4 reports the correlation between our persistence measures. They are highly, but not perfectly, correlated.

ρ

σ2C,5 σ2C,1

σ2C,5 σ2C,1

.735

σ2pers σ2tot

.839 .538

Table 2.4. Correlation between persistence measures using sector TFP data.

56

Investment regression on sector level We first estimate the investment regression (R0) on 3-digit SIC sector values. Following Fazzari et al. (1988) we use a fixed eﬀects approach and assume homoskedasticity. Some later work has used the one period lagged values of the explanatory variables as instruments to avoid potential bias due to measurement error in q˜ (Angelopoulou (2004)).9 But potential bias in the level of the coeﬃcient is irrelevant for our purposes, as we only care about diﬀerences between them. We have no reason to believe this potential bias would diﬀer between the groups we are studying. Before presenting coeﬃcients of regression (R0) per group using a sample split, we report the full sample estimates in Table 2.5.

Coeﬃcient a1

0.099 (.057)

a2

0.643 (.016)

Table 2.5. Full sample estimates of (R0). n=2.214, 89 sectors. The coeﬃcient a2 (on cf ) is substantially larger than firm-level estimates of the same coefficient, both compared to the literature and estimates in the present paper. We create sample splits and report results using all three persistence measures. In Table 2.6 we present the results from estimating (R0) using the sample split. 9

Due to the timing restriction in our two other approaches the method with lagged explanatory variables is not usable for those. To be consistent we use the simple estimation method also for our first approach.

57

Grouping variable Coeﬃcient Group 1 ρ

σ 2C,5 /σ 2C,1

σ 2pers /σ 2tot

Group 5

a1

-.437 (.283)

.055 (.021)

a2

1.468** (.061) .566 (.028)

a1

-.206 (.139)

a2

5.103** (.103) .657 (.038)

a1

-.445 (.276)

a2

1.469** (.063) .466 (.027)

.088 (.026)

.019 (.015)

Table 2.6. Estimates from regression (R0) on sector values. Grouped by TFP persistence from NBER-CES. n=2.214, 89 sectors. Pairwise significant diﬀerence between group 1 and group 5, at the 95% confidence level denoted by **. We have the same result for all three grouping variables: A large, insignificant and negative estimate of a1 (the coeﬃcient on q˜) for group 1, while group 5 has a “standard” value of a1 : small and positive. The coeﬃcient for cf, a2 , is significantly larger for group 1 than for group 5. All of these estimates, and their diﬀerences between groups, are in line with the predictions of the LW model. The most striking result is the negative estimates of a1 for group 1. These results should be interpreted with caution, mainly because the investment regression (R0) normally is estimated on the firm-level, which we do next.

Investment regression on firm level The full sample estimates are reported in Table 2.7 and the sample split results in Table 2.8.

58

Coeﬃcient a1

.0663 (.0027)

a2

.0909 (.0033)

Table 2.7. Full sample estimates of (R0). n=19.256. The full sample estimates are roughly in line with estimates in the literature (e.g. Gilchrist and Himmelberg (1995)), although the estimate of a2 normally is higher than here.

Grouping variable Coeﬃcient Group 1 ρ

σ 2C,5 /σ 2C,1

σ 2pers /σ 2tot

Group 5

a1

.0714 (.0080)

.0683 (.0053)

a2

.1408** (.0097) .0706 (.0063)

a1

.0487** (.0088) .0916 (.0091)

a2

.1428 (.0087)

.1314 (.0098)

a1

.0686 (.0079)

.0643 (.0049)

a2

.1373** (.0099) .0725 (.0060)

Table 2.8. Estimates from regression (R0) on firm values. Grouped by TFP persistence from NBER-CES. n=19.256, 89 sectors. Pairwise significant diﬀerence between group 1 and group 5, at the 95% confidence level denoted by **. The results are weakly supportive of the LW model: for grouping by ρ or

σ 2pers σ 2tot

the estimated

a2 is significantly lower for group 5 than for group 1 as predicted, but there is no diﬀerence in a1 . For grouping by

σ 2C,5 σ 2C,1

instead a1 is significantly diﬀerent between groups in the predicted

direction, but a2 is similar across groups. We performed the same exercise at the 4-digit SIC level. Unfortunately this means that the persistence estimates get very imprecise as each estimate is based on only one time-series. 59

As above, we perform a pairwise test to see whether ρˆi is significantly diﬀerent than ρˆj . Using a 95% confidence interval, the lowest ρˆi is only significantly diﬀerent from 25 of the 130 other estimates. Out of 8515 pairwise comparisons, 150 of the ρˆi are significantly diﬀerent from each other. We conclude that the persistence estimated at this level is not useful in distinguishing between groups of firms, and do not report the full investment regression results (they are very mixed, mainly supportive for a2 , and not supportive for a1 ). Persistence measures for firm level data The model contains sector-specific productivity shocks, so we choose to estimate persistence per sector, also when using firm level data. This also has the added advantage of yielding tighter estimates of persistence as it allows us to exploit the panel structure of the data. Table 2.9 presents the three persistence estimates for log labor productivity per 4-digit SIC sector (after a deterministic time trend has been taken out).10

Parameter Mean Cross-sectoral standard deviation Std.error ρ

.524

.216

.0993

σ2C,5 σ2C,1

.506

.227

.267

σ2pers σ2tot

.273

.172

n/a

Table 2.9. Estimates of persistence of firm-level labor productivity, by 4-digit SIC. n=31.267. 188 sectors. With a 95% confidence level., the lowest ρˆ is significantly diﬀerent from 183 of the 187 other estimates. Out of 17578 pairwise comparisons, 7055 of the ρˆ are significantly diﬀerent from each other. We conclude that, in terms of significant diﬀerence between sectors, these estimates are superior to the sector data estimates used above. 10

σ2

In terms of estimating the σpers parameter of the LW model, Table 9 provides a lower bound. As opposed 2 tot to in Table 2, here we capture the additional shocks (on top of technology). Unfortunately, we also capture firm-level idiosyncratic shocks, and measurement error, that do not have any counterpart in the LW model.

60

Table 2.10 report the correlation between our persistence measures. They are highly, but far from perfectly correlated.

ρ

σ2C,5 σ2C,1

σ2C,5 σ2C,1

.514

σ2pers σ2tot

.566 .656

Table 2.10. Correlation between persistence measures using firm-level labor productivity data. Investment regression results In Table 2.11 we present the results from estimating (R0) using the sample split per group.

Grouping variable Coeﬃcient Group 1 ρ

σ 2C,5 /σ 2C,1

σ 2pers /σ 2tot

Group 5

a1

.0669 (.0052) .0489 (.0039)

a2

.0220 (.0045) .0484 (.0051)

a1

.0693 (.005)

a2

.0698 (.0045) .0577 (.0057)

a1

.0735 (.0045) .0693 (.0040)

a2

.0156 (.0034) .0436 (.0057)

.0591 (.0040)

Table 2.11. Estimates from regression (R0) on firm values. Grouped by labor productivity persistence from Compustat. n=31.267. 188 sectors. With grouping by ρ or

σ2pers , σ2tot

the results are opposite to the prediction of the LW model: a1

is lower for group 5 than group 1, and a2 is higher for group 5 than for group 1. If we instead group by

σ2C,5 , σ2C,1

a2 does change in the predicted direction, but the diﬀerence is insignificant.

61

We perform the same exercise using the persistence of the Sales/Capital ratio to group sectors. There is no apparent time trend in this variable, so we estimate the persistence of the raw, undetrended values. The level and standard deviation of the persistence is similar to the estimates for labor productivity, and are not reported. The results for the investment regression (R0) are presented in Table 2.12: Grouping variable Coeﬃcient Group 1 ρ σ2C,5 σ2C,1

σ2pers σ 2tot

Group 5

a1

.0553 (.0029) .0420 (.0040)

a2

.0160 (.0025) .0439 (.0049)

a1

.0730 (.0047) .0529 (.0034)

a2

.0407 (.0037) .0600 (.0045)

a1

.0740 (.0037) .0524 (.0048)

a2

.0261 (.0040) .0185 (.0039)

Table 2.12. Estimates from regression (R0) on firm values. Grouped by Sales/Capital persistence from Compustat. n=31.267. 188 sectors. As can be seen from Table 2.12, the estimates using grouping by ρ or

σ2C,5 σ2C,1

does not support

the LW model: the size ordering of a1 and a2 between groups are opposite to the predicted.11 If we instead group by

σ 2pers σ 2tot

the model is supported, insignificantly, by the diﬀerence in a2 between

group 1 and group 5. To summarize the results of using this approach of grouping sectors by persistence, we find mixed support for the LW model. The sector level investment regression confirms exactly the implications of the LW model, but it is more common to run the investment regression on the firm level. We did this and again found support for the LW model, although weaker. Finally, for the estimates of persistence based on firm-level data there is no support for the model. 11

We note that this negative result is driven by firms with very low cf . If we exclude firms with cf < −1, the comparison between groups of both a1 and a2 support the LW model, although insignificantly.

62

2.4.4

Grouping by comovement of q˜ and i

In this second approach, and in the third approach, we test the LW model on the firm-year observation level, not on the sector level as above. To do this we use only firm-level data from the Compustat dataset. Recall that the LW model implies that if a persistent shock hits, q˜ and i move in the same direction, and if a temporary shock hits they move in opposite directions. Although in the LW model positive and negative shocks to productivity have symmetrical impact, the true empirical relationship may be asymmetrical. We therefore also separate positive shocks from negative shocks, using the sign of ∆iit , so that we are able to distinguish between these two issues. We end up with four groups of ∆˜ qit observations: Group 1. Positive change in both q˜ and i, ∆˜ q > 0 & ∆i > 0. Group 2. Negative change in both q˜ and i, ∆˜ q < 0 & ∆i < 0. Group 3. q˜ and i moving in diﬀerent directions and ∆i is positive, ∆˜ q < 0 & ∆i > 0. Group 4. q˜ and i moving in diﬀerent directions and ∆i is negative, ∆˜ q > 0 & ∆i < 0. Following the discussion in section 2.2.6 relating to Figure 2.1, the model predictions for the type of shock for each group is summarized in Table 2.13. These predictions are what we test below.

Group Definition

Type of shock predicted by model

1

∆˜ q > 0, ∆i > 0 positive persistent

2

∆˜ q < 0, ∆i < 0 negative persistent

3

∆˜ q < 0, ∆i > 0 positive temporary

4

∆˜ q > 0, ∆i < 0 negative temporary

Table 2.13. Groups of observations, and their predicted type of shock.

63

Each firm-year observation belongs to one of the above four groups. A firm does not belong in one specific group. As a first step we look at the average future growth rates for each of the four groups, mainly to check that each shock is of the predicted type. Second, we compare the predictive value of changes in q˜ for future productivity growth between the above four groups. We use a method that is very similar to a sample split, except for some technical details.12 We estimate the following regression separately for each group G=1,2,3,4:

∆k+1 ait+k = αG + β G ∆˜ qit + ui + εit

(R1)

where ∆k+1 ait+k denotes the growth rate of the labor productivity for firm i from year t − 1 to year t + k (k=4 in the base case), ui denotes firm fixed eﬀects. As an alternative proxy for profitability we use sales growth, ∆k+1 sit+k . In a standard Tobin’s q model ∆˜ q predicts future growth of sales or profitability, here proxied by sales or labor productivity, implying β i > 0. The LW model has more specific implications, as shown above. It predicts β 1 > 0 and β 2 > 0 as the comovement between q˜ and i indicate a persistent shock. Further, the LW model implies that the predictive value of ∆˜ qit is higher for observations where q˜ and i move together, i.e. β 1 > β 3 , β 1 > β 4 and β 2 > β 3 and β 2 > β 4 . If we allow diﬀerential impact of positive and negative changes in q˜ the only remaining implications for the coeﬃcients are β 1 > β 4 and β 2 > β 3 . Traditional q theory, without collateral constraints, predicts equal values for each of these coeﬃcients (and it further counterfactually predicts that q˜ should always comove positively with i). 12 The only diﬀerence vs. a pure standard sample split is that we calculate firm fixed eﬀects over the full sample.

64

Group results We start by calculating at the average growth rates for the four groups to check if they are in line with the model predictions. We graph the growth rates from time t − 1 of the variables that proxy for profitability, as deviations from their mean. 2.0%

1.5%

1.0%

Group 1, ∆q>0 & ∆i>0

0.5%

Group 2, ∆q0

4%

Group 2, ∆q β 3 for both proxies for profitability. The diﬀerence in the size between the β 0i s in each of these comparisons is statistically significant at least at the 90% confidence level. We note that this result is robust to changing the particular specification of the regression - the predicted relationships β 1 > β 4 and β 2 > β 3 hold for all the diﬀerent specifications that we estimate below. For robustness we run the same regression on all sectors in the dataset, including nonmanufacturing sectors. As seen in Table 2.15 the results are very similar.

Coeﬃcient \ dependent variable labor productivity sales β1

.07358∗ (.01872)

.4267∗∗ (.02857)

β2

.06042∗ (.01747)

.002223∗ (.02665)

β3

.008843 (.01753)

−.08247 (.02675)

β4

.01966 (.01943)

.2518 (.02965)

Table 2.15. All sectors, year ≥ 15, k=4 (n=36.959). These results, in terms of size ordering between the coeﬃcients, are unchanged for the 67

following three alternative specifications: Changes in k, the number of years into the future that we measure profitability, for k=3 and k=5, or changing the sample to the lowest possible required number of observations per firm (6), or for a high required number of observations (25). A potential issue with these results would if the labor productivity and sales growth that we observe is actually caused by investment, not by the exogenous shock. In terms of averages per group Figure 2.A1 of Sales/Capital growth removes this doubt as it shows large diﬀerences in the productivity of capital. Nevertheless, to check that our regression results are not driven by investment, we include investment growth as an explanatory term14 :

Coeﬃcient \ dependent variable labor productivity sales β1

.08760∗

.38286∗∗

β2

.06535∗∗

−.02802∗∗

β3

−.02112

−.11068

β4

.00728

.23287

coeﬃcient on ∆i

−.00757 (.00342)

.05863 (.00547)

Table 2.16. Manufacturing only, year ≥ 15, k=4 (n=20.436), with investment. We note that the estimates of βˆ i change only marginally,15 and their size ordering is unchanged. Still, the large and significant coeﬃcient on i for the regression with sales as the dependent variable is a clear sign that current investment, not surprisingly, aﬀects future sales growth. To sum up the results of the second approach, regression (R1) provide support of the LW model. The evidence from group average growth is instead very mixed: labor productivity 14

The coeﬃcients are only marginally aﬀected if we instead include investment in levels, or the sum of investment at time t, t+1, t+2 and t+3. The size ordering is unchanged, and the diﬀerence between the coeﬃcients remain significant. 15 Standard errors are very close to the original regression, and have been omitted to preserve space.

68

growth, presented in Figure 2.2, is not in line with the predictions of the model, while sales growth, presented in Figure 2.3, fully confirm the model predictions.16

2.4.5

Grouping by growth

Our third approach consists of grouping observations by productivity growth. Recall that the main implication of the LW model is that q theory holds conditional on persistent shocks, and is violated conditional on temporary shocks. We test this implication by using extreme values of productivity growth, of either sign, as a proxy for persistent shocks. To test the above implication of the model we regress i on q˜ and cf , just as in (R0) in the first approach above. The diﬀerence is that this time we create a sample split using the firm-year observation level. We use growth in labor productivity from t-2 to t+k, ∆k+2 ait+k , to divide the observations into five groups. The reason that we measure productivity starting from time t-2 is that the value of q˜it−1 we use in the regression must be from after the shock has hit.17 As an alternative grouping variable we use sales growth. We do not literally use a sample split, but instead run the following regression with dummies, where Il denote a dummy which is equal to 1 for group l, and 0 otherwise:

iit = a0 +

4 X l=1

al Il +

5 X

bl Il q˜it−1 +

l=1

5 X

cl Il cfit + ui + vt + eit

(R2)

l=1

The LW model predicts that for persistent shocks, proxied by extreme values of ∆k+2 ait+k , q theory should perform better than for temporary shocks, proxied by intermediate values of ∆k+2 ait+k . This means that the coeﬃcient on q˜, bl , for the extreme groups (group 1 and group 5) 16

There is an alternative interpretation of the result of this approach. Instead of attributing a negative comovement of observed q and investment to temporary shocks, one could argue that these observations represent stock market noise, or even irrationality. For this interpretation, note that managers control investment while the stock market, through the numerator of observed q (market value) generates the main part of the variation in observed q. Only when managers and the stock market participants update their expectations about the future profitability of the firm in the same direction, so that observed q and investment move together, does observed q have predictive value for future productivity. 17 This also means that we can not use instruments from earlier than t-1 to instrument for q˜.

69

should be higher than for the intermediate groups, and in particular for group 3. The opposite applies to the coeﬃcients on cf - cl should be smallest for group 1 and group 5, as q theory supposedly holds for these groups. Results The results for our estimation of (R2) with k=4 are presented in Table 2.17.

coeﬃcient \ grouping variable labor productivity

sales

b1

.04182 (.00412)

.06546** (.00638)

b2

.04592 (.00414)

.03696 (.005414)

b3

.03524 (.00435)

.02439 (.00458)

b4

.05640 (.00398)

.03468 (.00385)

b5

.04896 (.00353)

.04293** (.00300)

c1

.1086** (.00642)

.03267** (.00435)

c2

.1267 (.00811)

.11010 (.00941)

c3

.1620 (.00840)

.17179 (.0112)

c4

.06133 (.00593)

.12630 (.00861)

c5

.05222** (.00557)

.13416** (.00630)

Table 2.17. Estimates from regression (R2). Manufacturing only, year ≥ 15, k=4, n=18.993. Pairwise significant diﬀerence between extreme group and group 3 at the 95% level denoted by **. For grouping by labor productivity, this regression oﬀers limited support of the LW model. The estimates of bi are similar across groups and there is no clear pattern of lower coeﬃcients on q˜ for the intermediate groups, although b3 is the lowest coeﬃcient as predicted. But, the coeﬃcients ci for cf vary in the predicted way forming a inverted U-shape pattern with c3 at the peak. The pairwise diﬀerence between c3 and the extreme c0i s is significant at the 95% level.

70

For grouping by sales growth the results are supportive of the LW model in that firmyear observations with extreme values of productivity growth, as a proxy for persistent shocks, behave closer in line with q theory.18 As predicted, the five bi coeﬃcients form a symmetrical Ushape where b3 is the smallest and b1 and b5 are the largest. The pairwise diﬀerence between b3 and the extreme b0i s is significant at the 95% level. The ci coeﬃcients also follow the prediction of the model and, except for c4 < c5 , form a inverted U-shape with c3 as the largest coeﬃcient. The pairwise diﬀerence between c3 and the extreme c0i s is significant at the 95% level. For robustness we also run the regression (R2) without cf . The results (not reported) are unchanged: for grouping by labor productivity the bi coeﬃcients are almost indistinguishable, while for grouping by sales the U-shaped pattern remain. Results (not reported) are also qualitatively unchanged when we estimate regression (R2) for k=3 and k=5.

2.5

Conclusion

In this paper we have tested the main implication of the Lorenzoni and Walentin (2005) model and estimated the key parameter of it. This estimation confirmed that there is a substantial amount of temporary shocks to sector level productivity, although not as much as the Lorenzoni and Walentin model needs to explain the low correlation between Tobin’s q and investment. In terms of testing the model, we first the tested the implication of the model that Tobin’s q theory performs better for sectors with more persistent productivity processes. We did this by running the Fazzari et al. (1988) investment regression on a sample split where firms had been grouped according to the persistence of their respective sector productivity. The prediction of the model was confirmed using sector data, but found no support using firm-level productivity data. Second, we confirmed the implication of the model that persistent shocks to productivity, as opposed to temporary shocks, imply a positive comovement between observed q and investment. 18

It should still be noted that all coeﬃcients on cf, for all groups and regardless of grouping variable, are significantly diﬀerent from 0 (t-value>10), so the standard argument rejecting q theory applies to all groups.

71

Specifically, what we showed was that positive comovement between observed q and investment indicates that a persistent productivity shock has hit the firm, while a negative comovement indicates a temporary shock. This result is clear if we use sales growth as a proxy of persistent shocks, but weak if we use labor productivity growth. Third, we again ran the standard investment regression, this time on a sample split where firm-year observations had been grouped according to their productivity growth, as a proxy for persistent productivity shocks. The predictions of the model were only weakly confirmed when we grouped using labor productivity growth, but strongly confirmed when we grouped using sales growth. To sum up, the empirical results of this paper is weakly supportive of the Lorenzoni and Walentin (2005) model. Hopefully future work can better identify persistent and temporary shocks to profitability so that sharper results can be obtained.

72

APPENDIX 1: Proof of Proposition 2 (sketch) To analyze the stability properties of the steady state we can linearize the transition equation (1.8) and use the definition of Rt . We get the following second order equation for kt+1 = ˆ ln Kt − ln K, α2 kt+2 + α1 kt+1 + α0 kt = 0 where α2 = βθξ ´ i h ³ ˆ α−1 − (1 − γ) (1 − θ) ξ α1 = − ξ + 1 − βθR + βθ ξ + α (1 − α) K h i ˆ α−1 + (R − ξ) (1 − γ) (1 − θ) α0 = ξ + α (1 − α) (γ − (1 − γ) (1 − θ)) K Provided that α21 − α0 α2 > 0

(1.A1)

ˆ is saddle-path stable. Then with bounded shocks it is possible to show that the steady state K we can construct a stable stochastic steady state K. One can then establish the continuity of the function φ with respect to the parameters A (s) and show that φt is bounded in [φ, φ]. Finally, it is possible to find a small enough value of A − A such that the bounds for φt satisfy φ > γ + (1 − γ) φ. This guarantees that the financial constraint is always binding.

73

APPENDIX 2.1: Estimation of AR(1) process with i.i.d. shock on top Start from a detrended, stationary series of log productivity ait . Assume that the true process is: ait = xit + η it xit = ρxit−1 + εit with xit and η it both mean zero, i.i.d. and orthogonal to each other. The problem is to identify xit and η it separately. 1) Estimate ρ and V ar(xit ) by regressing ait on its own one period lag. Ignoring η it here is ok as we assumed η it are i.i.d. and orthogonal to εit , so the estimates will not be biased. 2) Derive an expression for σ 2η in terms of ρ and the autocovariance of ait . Rewrite ait as ait = ρait−1 + ˆεit + ηˆit where ˆεit = εit + η it ηˆit = −ρη it−1 Then the autocovariance of ait is: Cov(ait , ait−1 ) = ait ait−1 + 0 + 0 = = ρ2 Cov(ait−1 , ait−2 ) + ρ2 η 2it−1 Note that η 2it−1 = σ 2η . We use stationarity to rewrite the expression as σ 2η =

1 − ρ2 Cov(ait , ait−1 ) ρ2

We already know ρ and we can easily calculate Cov(ait , ait−1 ) and get σ 2η . 74

Finally the fraction of the variance of productivity that comes from persistent shocks can be calculated as

σ 2pers σ 2x σ 2ε /(1 − ρ2 ) = = σ 2tot σ 2x + σ 2η σ 2ε /(1 − ρ2 ) + σ 2η

75

APPENDIX 2.2: Figure

15% Group 1, ∆q>0 & ∆i>0 Group 2, ∆q

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