Sunk costs, profit variability, and turnover.

Gschwandtner, Adelina ; Lambson, Val E.

I. INTRODUCTION

The dynamic competitive approach to the study of industrial organization highlights the role of sunk costs and the associated hysteresis effects in determining how industries behave over time. The theoretical models are inherently difficult. Commenting on his own work, Jovanovic (1982, 651) remarked that "a curious feature of the paper is that proofs of 'obvious' results are complicated." Such complexity precludes a canonical dynamic competitive model but favors the development of various models focusing on different aspects of reality.

In spite of this, the dynamic competitive approach has yielded some predictions that are intuitively compelling and consistent with a variety of dynamic competitive models. Two such predictions are the focus of this article: industries exhibiting higher sunk costs should also exhibit greater intertemporal variability of firm-level profit and lower intertemporal variability in the number and identity of active firms. Examples of models that are broadly supportive of these predictions include those by Dixit (1989), Lambson (1991, 1992), and Hopenhayn (1992).

Dixit (1989) developed a continuous time model of a single firm facing an exogenous output price that follows a geometric Brownian motion. If entry costs are sunk, then the firm's entry-provoking price, say [alpha], exceeds the firm's exit-provoking price, say [omega]. Furthermore, [alpha] is increasing and [omega] is decreasing in the sunk cost, suggesting that the range of profit is greater if sunk costs are higher. This firm-level model is poorly suited for studying industry-level questions of entry and exit, but Caballero and Pindyck (1996) considered an industry-level extension of Dixit's model (1989, 657-58) and concluded that higher sunk costs increase the variability of the output price (and hence of profit) and decrease turnover.

Lambson (1992) constructed a discrete time model of an industry that is subjected to exogenous stochastic shocks that are common to the firms. Such shocks might include changes in input prices, demand conditions, and the regulatory environment, among others. Firm values above the entry cost [xi] induce entry whereas firm values below the scrap value [chi] induce exit. The intertemporal range of firm values is thus approximately [xi]-[chi], which is also a natural definition of sunk costs in the model. With the intertermporal range of firm value being thus identified with sunk cost, if the range of current profit is positively related to the range of firm values, then the range of profit will be higher in high sunk cost industries, yielding the first prediction. Less obvious but no less true in this model is the proposition that the intertemporal range of the number of active firms will be lower in high sunk cost industries. Lambson (1991) allows for endogenous heterogeneity because entering firms pay a sunk cost to install one of several available technologies. This generates simultaneous entry and exit when, for example, there is a large change in relative input prices. General proofs are lacking, but examples suggest that higher sunk costs will tend to coexist with higher variability of profit and lower turnover.

Hopenhayn (1992) modeled an industry in discrete time where firms are buffeted by idiosyncratic shocks to their productivity. Firms that suffer a series of negative shocks suffer such a decrease in their productivity that they find it optimal to exit the market. The productivity level that triggers exit is lower when the entry cost is higher. The lower trigger level implies a lower rate of turnover. It also implies that a firm's profit can be lower without provoking exit; this suggests that high sunk cost industries will exhibit more variability in firm-level profits over time.

II. EMPIRICAL PRECEDENTS

Section I reviews two predictions from the theoretical literature using dynamic competitive models: intertemporal profit variability should be higher in higher sunk cost industries, and turnover should be lower in higher sunk cost industries. Empirical work relevant to the first result is sparse. (1) By contrast, there is a substantial empirical literature devoted to entry and exit rates. An early effort, perhaps inspired by Caves and Porter (1976), was due to Deutsch (1984), who found what can be interpreted as evidence that exit is negatively related to sunk costs. In an ambitious study, Dunne et al. (1988, 1989) analyzed the patterns of firm entry and exit in U.S. manufacturing industries over the periods 1963-1982 and 1967-1977. They found a high and positive correlation between entry rates and exit rates, as well as substantial and persistent differences in these rates across industries. Geroski et al. (1990) did a summary and interpretation of much of the earlier work. Subsequent research explored the empirical relationship between proxies for sunk costs (such as measures of economies of scale or capital intensity) and entry and exit rates. There are examples in work by Geroski and Schwalbach (1991), Siegfried and Evans (1992, 1994), and Audretsch (1995). Curiously, most analysis yielded either no relationship or counterintuitive positive relationships. Audretsch (1995) remarked, "One of the most startling results that has emerged in empirical studies is that entry into an industry is apparently not substantially deterred or even deterred at all in capital-intensive industries in which scale economies play a role" (46). More recently, Disney et al. (2003) analyzed entry, exit, and establishment survival in U.K. manufacturing. They also found strong correlation between industry entry rates and industry exit rates. They hypothesized that entry and exit rates might be correlated because industries differ in their sunk costs, but the authors did not explore this further. Using international data, Gschwandtner and Lambson (2002) found the intertemporal variability of the number of firms to be lower in industries where proxies for sunk costs (namely, capital costs and capital costs per worker) were higher.

In what follows, we present simple tests of the two robust theoretical propositions described in section I. First we test for a positive relationship between proxies for sunk costs and intertemporal profit variability using a new data set constructed by combining Compustat data with data from Moody's Industrial Manual (1954-2001). Next, we test for a negative relationship between turnover and proxies for sunk costs--an intuitively and theoretically compelling but heretofore poorly documented phenomenon--using annual data from the U.S. Census Bureau.

III. EMPIRICAL SPECIFICATIONS AND DATA

Intertemporal Profit Variability

In this section we explore the relationship between the intertemporal variability of profit and sunk costs. We use a new data set constructed by supplementing Compustat data with data from Moody's Industrial Manual. Specifically, gaps in the former--a particularly common problem in the early years--were filled from the latter. The result is a set of annual observations from 1950 through 2001 for 162 firms in the United States. The 162 firms were among the largest 500 in terms of sales in 1950 and managed to survive until 2001. Although there is obvious selection bias, it is irrelevant to the question because theory predicts more variable profitability among surviving firms in high sunk cost industries.

The variables used are Net Income (data18); Total Assets (data6); and Net Total Property, Plant, and Equipment (data8). Net Income represents the income of a company after all expenses--including special items, income taxes, and minority interests--but before provisions for common and preferred dividends. The Total Assets variable represents current assets plus net property, plant, and equipment plus other noncurrent assets. The Net Property, Plant, and Equipment variable sums the cost of tangible fixed property used in the production of revenue, less accumulated depreciation. (2) All the values are real, having been adjusted by the gross domestic product deflator with 1950 as the base year.

We used Net Income as a proxy for profit. (3) We measured intertemporal variability in two ways: the range and the variance. Although theory favors the range as the appropriate measure, the range is sensitive to outliers. In any case, the regressions with range and the regressions with variance yield similar results.

We used the intertemporal mean of a firm's Net Property, Plant, and Equipment variable as a proxy for a firm's sunk cost. This is a good proxy to the extent that the capital stock is industry specific and is an important component of the firms' sunk costs. Of course, it is not a perfect measure of sunk cost. For one thing, it ignores noncapital start-up costs, such as the opportunity cost of entrepreneurial time, initial legal fees, the cost of market research, and so on. Furthermore, it does not adjust for the timing of the sunk costs. In reality, firms pay an initial entry cost to build a plant and then make ongoing adjustments. However, it is plausible that this variable is highly correlated with sunk costs and is hence a reasonable proxy.

Now, large firms are likely to exhibit greater intertemporal variability simply because of their size: for example, a two-plant firm will exhibit twice the variability of a one-plant firm if the plants are identical. To control for size, in some specifications we divided a firm's sunk cost proxy by its total assets and then calculated the intertemporal mean of that ratio. To further control for size we included the intertemporal mean of a firm's income. The various specifications with the range of profit as the dependent variable are listed in equations 1-6. (The specifications with the variance of profit as the dependent variable are similar.)

(1) Log [Range.sub.i]([[pi].sub.it]) = [alpha] + [[beta].sub.[xi]][K.sub.i] + [epsilon]

(2) Log [Range.sub.i]([[pi].sub.it]) = [alpha] + [[beta].sub.[xi]][(K/A).sub.i] + [epsilon]

(3) Log [Range.sub.i]([[pi].sub.it]) = [alpha] + [[beta].sub.[xi]]Log[(K).sub.i] + [epsilon]

(4) Log [Range.sub.i]([[pi].sub.it]) = [alpha] + [[beta].sub.[xi]]Log[(K/A).sub.i] + [epsilon]

(5) Log [Range.sub.i]([[pi].sub.it]) = [alpha] + [[beta].sub.[xi]]Log[(K).sub.i] + [[beta].sub.[theta]][[PI].sub.i] + [epsilon]

(6) Log [Range.sub.i]([[pi.sub.it]) = [alpha] + [[beta].sub.[xi]]Log[(K/A).sub.i] + [[beta].sub.[theta]][[PI].sub.i] + [epsilon]

Here [[pi].sub.it] is the net income of firm i in year t; [Range.sub.i]([[pi].sub.it]) is the intertemporal range of company i's profit; [K.sub.i] is the firm's intertemporal mean of the sunk cost proxy; [(K/A).sub.i] is the intertemporal mean of the sunk cost proxy divided by total assets of firm i; and [[PI].sub.i] is the mean of net income for each company over the period 1950-2001. Regression results are in Table 1. Some descriptive statistics are in Table 4.

Turnover

To explore the relationship between the rate of turnover and sunk costs, we used annual data from the U.S. Census Bureau. Turnover was defined as (Entry + Exit)/2 for each industry in each year. With sponsorship from the U.S. Small Business Administration, the Census Bureau collects data on entry and exit by industry for the United States as a whole and for each state. (4) This database contains information about entry, exit, and employment from 1990 to 2000 for each included industry. (5)

Time series from 1994 to 2001 (eight years) are available in the U.S. Census Bureau's Annual Capital Expenditures Survey. (6) Categories used in the survey comprised primarily three-digit and selected four-digit industries from the North American Industry Classification System for the more recent years. The period that is available for both variables is 1994-2000 (seven years). (7)

The database has two advantages compared to previous studies that use census data with observations at five-year (or at best two-year) intervals. First, annual observations reflect more accurate information about entry and exit. Second, whereas most previous studies brought evidence only from the manufacturing sector, (8) the present database includes observations from mining, construction, transportation, communication, utilities, and finance.

We considered two different proxies for sunk costs: "Total Capital Expenditures for Structures and Equipment for Companies with Employees" divided by the number of Employees (K/L) and "New Capital Expenditures for Structures and Equipment for Companies with Employees" divided by the number of Employees (New K/L). The total capital expenditures variable, K, is similar to the Net Property, Plant, and Equipment variable of the previous subsection and suffers from the same advantages and shortcomings. The difficulties arising from the timing issues are mitigated in the alternative specification using the New Capital Expenditures variable. The two variables yield similar results. By looking at capital intensiveness relative to labor, we partially control for size. However, it was still conceivable that this was not sufficient, so we added employment as a separate control for the size of the industry. In summary, we used the following specifications:

(7) logT = [gamma] + [eta]K/L + [mu]

(8) logT = [gamma] + [eta]NewK/L + [mu]

(9) logT = [gamma] + [eta]K/L + [theta]L + [mu]

(10) logT = [gamma] + [eta]NewK/L + [theta]L + [mu],

where logT is the logarithm of turnover in the industry, L is the number of employees in the industry, and K/L and NewK/L are the two proxies for sunk cost. We did the analysis separately for each year as well as for all the years combined. Regressions results are in Tables 2 and 3. Some descriptive statistics are in Tables 4.

IV. EMPIRICAL RESULTS

The results for the relationship between the intertemporal variability of profit and sunk costs are summarized in Table 1. Theory suggests a positive correlation between the intertemporal variability of a company's profit and a proxy for the company's sunk costs. The coefficient of the sunk cost proxy is positive and significant at the 5% level or better in all specifications. The reported standard errors are cluster corrected by industry. (9)

The results for the relationship between the rate of turnover and sunk costs are presented in Table 2 (specifications 7 and 8) and Table 3 (specifications 9 and 10). Theory suggests a negative relationship between the rate of turnover and sunk costs. In each of the seven years and in the aggregated sample, all specifications generate a negative coefficient that is statistically significant. (10) When we introduce in the regression the total number of employees in the industry to control for size, the results remain significant. The coefficients of the measure of size are significantly positive. We conclude that the empirical evidence is consistent with the aforementioned predictions from the theoretical literature.

V. CONCLUDING REMARKS

This analysis suggests that profits are more volatile, and turnover lower, in industries that exhibit higher sunk costs. The theoretical predictions cited in section I arise from dynamic competitive models without any distortions. Thus, equilibrium solves a social planner's problem of maximizing the expected present value of the sum of producer and consumer surplus, including the entry costs and scrap values. As argued by Lambson (1992) regarding differing long-run average profits across industries, differences in the volatility of profits and differences in turnover across industries fail to imply the existence of market imperfections. Thus, strictly speaking, the policy implications of this research lead to nonintervention. Of course, a plausible model with market imperfections might generate the same predictions with different policy prescriptions, but the nature of those prescriptions may well depend critically on the precise structure of the model.

REFERENCES

Audretsch, D. B. Innovation and Industry Evolution. Cambridge, MA: MIT Press, 1995.

Caballero R., and R. Pindyck, R., "Uncertainty, Investment, and Industry Evolution," International Economic Review, 37(3), 1996, 641-62.

Caves, R. E., and M. E. Porter. "Barriers to Exit," in Essays on Industrial Organization in Honor of Joe S. Bain, edited by R. T. Masson and P. D. Qualls. Cambridge: Ballinger, 1976, 39-69.

Deutsch, L. L. "An Examination of Industry Exit Patterns." Review of Industrial Organization, 1, 1984, 60-68.

Disney, R., J. Haskel, and Y. Heden. "Entry, Exit and Establishment Survival in UK Manufacturing." Journal of Industrial Economics, 51(1), 2003, 91-112.

Dixit, A. "Entry and Exit Decisions under Uncertainty." Journal of Political Economy, 97(3), 1989, 620-38.

Dunne, T., M. J. Roberts, and L. Samuelson. "Patterns of Firm Entry and Exit in U.S. Manufacturing Industries." Rand Journal of Economics, 19(4), 1988, 495-515.

--. "The Growth and Failure of U.S. Manufacturing Plants." Quarterly Journal of Economics, 104(4), 1989, 671-98.

Geroski, P., R. J. Gilbert, and A. Jacquemin. Barriers to Entry and Strategic Competition. Chur, Switzerland: Harwood Academic, 1990.

Geroski, P., and J. Schwalbach, eds. Entry and Market Contestability: An International Comparison. Oxford: Basil Blackwell, 1991.

Gschwandtner, A., and V. Lambson. "The Effects of Sunk Costs on Entry and Exit: Evidence from 36 Countries." Economics Letters, 77, 2002, 109-15.

Hopenhayn, H. "Entry, Exit and Firm Dynamics in Long Run Equilibrium." Econometrica, 60, 1992, 1127-50.

Jovanovic, B. "Selection and the Evolution of Industry." Econometrica, 50(2), 1982, 649-70.

Lambson, V. "Industry Evolution with Sunk Costs and Uncertain Market Conditions." International Journal of Industrial Organization, 9(2), 1991, 171-96.

--. "Competitive Profits in the Long Run." Review of Economic Studies, 59, 1992, 125-42.

Lambson, V., and F. Jensen. "Sunk Costs and the Variability of Firm Value over Time." Review of Economics and Statistics, 77(3), 1995, 535-44.

--. "Sunk Costs and Firm Value Variability: Theory and Evidence." American Economic Review, 88(1), 1998, 307-13.

Moody's Investor Service, Moody's Industrial Manual, New York: Moody's Investor Service, 1954-2001.

Opler, T., and S. Titman, "Financial Distress and Corporate Performance," The Journal of Finance, 49(3), 1994, 1015-40.

Siegfried, J., and L. Evans. "Entry and Exit in U.S. Manufacturing Industries from 1977 to 1982," in Empirical Studies in Industrial Organization: Essays in Honor of Leonard W Weiss, edited by D. B. Audretsch and J. Siegfried. Ann Arbor: University of Michigan Press, 1992.

--. "Empirical Studies of Entry and Exit: A Survey of Evidence." Review of Industrial Organization, 9(2), 1994, 121-55.

(1.) Lambsonand Jensen (1995, 1998) documented positive correlation between the intertemporal variability of firm values and proxies for sunk costs.

(2.) For more detailed definitions of the data, see the Compustat Data Definitions.

(3.) Although it would be tempting to try to control for business cycles, the mechanism driving the predictions must hold independently of the business cycle. Times that are good induce entry, and times that are bad induce exit. It does not matter why times are good or bad.

(4.) These data are available at http://www.sba.gov/ advo/stats/data.html.

(5.) More specific information is at http://www.census. gov/csd/susb/susb2.htm#godyn1.

(6.) These data are available at http://www.census.gov/ csd/ace/ace-pdf.html.

(7.) Note that even if some studies use a longer period, the number of years is usually smaller because they use five-year census data.

(8.) See, for example, Audretsch (1995).

(9.) Because high leveraged firms are more risky and have a higher variation in profits, in some specifications we controlled for this by including a debt measure (short-term or long-term debt divided by total assets) into the regression. The coefficients stayed positive and significant. See Opler and Titman (1994),

(10.) The database for "New Capital Expenditures" is more recent, but the number of observations is sometimes smaller than it is for the "Total Capital Expenditures." It varies between 96 and 140 per year whereas the number of observations for the "Total Capital Expenditures" varies between 103 and 140 per year. The number of observations increases in both cases starting with the year 1999, when the North American Industry Classification System was introduced.

ADELINA GSCHWANDTNER and VAL E. LAMBSON, We are grateful to Jesus Crespo-Cuaresma, Burcin Yurtoglu and some anonymous referees for their helpful comments.

Gschwandtner: Universitat Assistent Magistrate Doctor, Department of Economics, University of Vienna, BWZ Bruennerstr. 72, A-1210 Vienna, AUSTRIA. Phone (00431) 4277 37480, Fax (00431) 4277 37489, E-mail adelina.gschwandtner@univie.ac.at

Lambson: Professor of Economics, Department of Economics, Brigham Young University, Provo UT 84602, USA. Phone (801) 422-7765, Fax (801) 422-0194, E-mail vlambson@byu.edu

TABLE 1
Dependent Variables: Logarithm of the Range of Company's
Income Equations 1-6, Logarithm of the Variance of Company's
Income Equations 7-13

Eq. K K/A LogK Log K/A

 1 0.0005 ***
 (9E-05)
 2 0.954 ***
 (0.319)
 3 0.828 ***
 (0.032)
 4 0.819 ***
 (0.267)
 5 0.728 ***
 (0.040)
 6 0.536 ***
 (0.203)
 7 0.0011 ***
 (2E-04)
 8 1.882 **
 (0.838)
 9 1.661 ***
 (0.088)
 10 1.607 **
 (0.675)
 11 1.432 ***
 (0.100)
 12 1.027 ***
 (0.386)
Eq. [PI] Adj. [R.sup.2]

 1 0.379

 2 0.041

 3 0.775

 4 0.043

 5 0.0009 *** 0.790
 (0.0003)
 6 0.0036 *** 0.460
 (0.0006)
 7 0.374

 8 0.041

 9 0.787

 10 0.041

 11 0.0021 *** 0.808
 (0.001)
 12 0.0075 *** 0.485
 (0.0012)

Note: K, [PI], and A are measured in millions of real dollars
(base year 1950) per firm. The number of observations is always
162. Regression is with heteroskedasticity and cluster correction
of standard errors. Numbers in parentheses are root square errors.

* p [less than or equal to] .10; ** [less than or equal to] < .05;
*** [less than or equal to] .01.

TABLE 2
Dependent Variable: logTurnover =
log[(Entry+Exit)/2] per Industry

Year K/L NewK/L Adj. [R.sup.2] Obs.

1994 -23.83 *** 0.068 105
 (8.11)
 -24.21 *** 0.064 105
 (8.49)
1995 -23.75 *** 0.080 105
 (7.51)
 -24.87 *** 0.101 97
 (7.23)
1996 -21.76 *** 0.068 103
 (7.49)
 -21.36 *** 0.065 96
 (7.75)
1997 -15.73 ** 0.045 108
 (6.39)
 -15.90 ** 0.045 108
 (6.50)
1998 -14.23 ** 0.039 108
 (6.23)
 -15.09 ** 0.039 108
 (6.52)
1999 -12.54 *** 0.046 140
 (4.52)
 -13.09 *** 0.046 140
 (4.70)
2000 -9.75 *** 0.040 140
 (3.73)
 -10.70 *** 0.025 140
 (4.02)
All -14.75 *** 0.055 809
 (2.14)
 -15.595 *** 0.058 794
 (2.22)

Note: K and NewK are measured in millions of current
dollars. Numbers in parentheses are root square errors.

* p [less than or equal to] .10; ** p [less than or equal to] .05;
*** p [less than or equal to] .01.

TABLE 3
Dependent Variable: logTurnover =
log[(Entry+Exit)/2] per Industry

Year K/L NewK/L L Adj. [R.sup.2] Obs.

1994 -15.66 ** 3.36E-07 *** 0.338 105
 (6.95) (5.13E-07)
 -15.86 ** 3.37E-07 *** 0.336 105
 (7.26) (5.14E-08)
1995 -16.29 ** 3.01E-07 *** 0.344 105
 (6.45) (4.63E-08)
 -17.83 *** 2.76E-07 *** 0.369 97
 (6.15) (4.29E-08)
1996 -13.47 ** 3.18E-07 *** 0.353 103
 (6.36) (4.71E-08)
 -13.12 ** 3.13E-07 *** 0.353 103
 (6.57) (4.78E-08)
1997 -9.14 * 3.36E-07 *** 0.333 108
 (5.43) (4.91E-07)
 -9.31 * 3.36E-07 *** 0.333 108
 (5.51) (4.91E-08)
1998 -7.37 ** 3.1E-07 *** 0.338 108
 (3.20) (4.54E-08)
 -8.11 ** 3.1E-07 *** 0.339 108
 (3.48) (4.53E-08)
1999 -7.04 * 4.14E-07 *** 0.351 140
 (3.78) (5.10E-08)
 -7.40 * 4.14E-07 *** 0.351 140
 (3.94) (5.10E-08)
2000 -5.26 * 4.16E-07 *** 0.359 140
 (3.09) (4.98E-08)
 -5.84 * 4.16E-07 0.360 140
 (3.34) (4.98E-08)
All -8.78 *** 3.43E-07 *** 0.346 809
 (1.80) (1.81E-08)
 -9.44 *** 3.38E-07 *** 0.350 794
 (1.87) (1.79E-08)

Note: K and NewK are measured in millions of current
dollars. Numbers in parentheses are root square errors.

* p [less than or equal to] .10; ** p [less than or equal to] .05;
*** p [less than or equal to] .01.

TABLE 4
Descriptive Statistics

 Standard
 Mean Median Deviation

Log [Range.sub.t]
 ([[pi].sub.t]) 2.068 2.088 0.603
K 374.714 163.579 686.728
K/A 0.364 0.337 0.128
Log K 2.139 2.214 0.641
Log K/A -0.465 -0.472 0.152
[PI] 59.328 23.421 107.351
T 11368.994 2689.5 22902.306
L 1748414.6 649823 3235491.29
K/L 0.018 0.007 0.032
NewK/L 0.017 0.007 0.031
LogT 7.76 7.90 2.02