the productivity and welfare effects of government r\u0026d in the u.s. softwood lumber industry

$: THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R\u0026D IN THE U.S. SOFTWOOD LUMBER INDUSTRY$
THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D

IN THE U.S. SOFTWOOD LUMBER INDUSTRY*

bY Barry J. SELDON

School of Social Sciences

University of Texas at Dallas

Richardson, Texas

and William F. HYDE

U.S. Department of Agriculture

Economic Research Service

Washington, D. C.

* The authors thank T. Dudley Wallace for many helpful comments and suggestions during the development of the economic approach. We thank Douglas Adie and an anonymous referee for comments on this paper. Ed Henneberger of the US. Department of Labor supplied the output data. Roy Boyd provided the hardware sales and the related price series. Sudip Banerjee assisted in data collection and computer programming. We thank Jeanne Danielson, George Harpool, Dave Lewis, and Ken Skog of the US. Forest Products Laboratory for providing information concerning R&D in the lumber industry and Gary Lindell of the Laboratory for his cooperation and assistance in collecting the R&D data series. The usual disclaimer applies.

240 B. SELDON & W.F. HYDE

Introduction

Empirical studies of R&D commonly suggest that government research is not so productive as private research (see, e.g., Griliches, 1987, and the survey in Levy and Terleckyj, 1989). Levy and Terleckyj (1983, esp. 557-9) find no significant effect of govlernment R&D on private productivity. They note that this is surprising since their measure of government R&D includes publicly funded agricultural research which is often found to increase private Productivity. Indeed, Ruttan (1980) lists many empirical studies which show very satisfactory returns to public agricultural research. Recently, however, Oehmke (1988) has shown that the agricultural returns-to- research literature produces upwardly biased estimates of the effect of public R&D due to distortions in the markets induced by various forms of government intervention.

Levy (1990) suggests that a zero coefficient associated with public research in a production function may be due to private firms equating the value of the marginal product of public research to the firms’ cost of utilizing that research. Since the government makes its findings freely available, the firms’ cost is zero and we should expect the value of the marginal product to be zero.’ This i:j plausible so long as government results are available in varying quantities without a binding constraint upon the individual firm. However, it seems more reasonable to suppose that government R&D is more discrete than continuous in nature: a firm can use a particular result of government R&D or not.*

Given the survey of results reported in Levy and Terleckyj (1989) and the suggestion by Oehmke (1988) that the positive results estimated in the agricultural R&D literature may be overly optimistic (and despite the mixed results of Levy for government R&D across industries and countries), the benefits of government R&D may be questioned. On the other hand, in contrast to the findings which cast doubt upon the productivity of government R&D, Seldon (1987) estimates the internal rate of return (ZRR) to U.S. government R&D in the softwood plywood industry, which is not subject to the

1 Levy points out that this does not mean that the monetized total benefits of government research are equal to zero. 2 Of‘ course, the firm can use various results in convex combinations, and by doing so can substitute among the results. But this does not negate the possibility that the firm would want to use more government R&D than is supplied by the government.

THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 24 1

distortions of agricultural markets noted by Oehmke(1988), and finds the IRR to be quite high. But this may be a special case: officials of the U S . Department of Agriculture Forest Service have indicated to us in private correspondence tha t they believe the success of the government's softwood lumber research was much greater than would be the case in general.

In this paper, we look at a different case, that of softwood lumber (SIC code 2421X3 Like softwood plywood, there has been a long history of government R&D in softwood lumber production and government distortions are absent. We follow the method of Seldon(1987) in determining the IRR to government research in softwood lumber. We then extend the method to calculate the marginal internal rate of return (MIRR) using parameters from the same econometric model used to estimate the IRR.' We may interpret the MIRR as the marginal productivity of investment in public research and the IRR as the average productivity. With this interpretation, the IRR i s 1) maximized if it is equal to the MIRR, 2 ) increasing if it is less than the MIRR, and 3) decreasing if it is greater than the MIRR. We find the IRR to be quite acceptable by usual standards, but not so spectacular as in the plywood case. The MIRR is positive but lower than the IRR, indicating that the government was somewhat overinvested in softwood lumber research.

1 Sawmill Technology

Sawmills and planing mills in the U.S. have enjoyed productivity gains over the last several decades as a result of technical improvements pioneered by both private and government r e~ea rch .~ Important changes have involved plant design, sawing machinery and blades, and lumber handling techniques. Debarking and chipping

3 Softwoods are used more often than hardwoods in production because softwood stumpage is less expensive and easier to transform into final goods. For instance, in 1987, there were 26.7 billion board feet of softwood lumber produced in the US. compared with 6.3 billion board feet of hardwood lumber (Statistical Abstract ofthe United States, 1989). 4 This extension is possible because the econometric model exploits duality between the production function and the cost function in order to uncover the supply function of the industry. 5 This discussion benefits from Duke and Huffstutler (1977), Horvath (1980), and correspondence with US. Forest Products Laboratory personnel.

B. SE'LDON & W.F. HYDE 242 -

machines were developed in the 1950's and 1960's and the sorting, stacking, and packaging of lumber became more automated. Nondestructive electromechanical stress graders allowed more efficient and precise grading of lumber. In t'he early 1960's mechanized carriages and kickers were introduced which allowed the sawyer t o manipulate logs more easily. In the late 1960's and early 1970's the computer began t o assume an important role in determining maximum yield from each log, setting the saw system, and controlling the movement of the log on the saw carriage.

US . Government R&D for wood products is performed a t the U.S. Department of Agriculture Forest Products Laboratory (FPL) in Madison, Wisconsin and associated regional experiment stations around the country. Much of the government research has concentrated upon creating higher yields. New edger saws were developed with a narrow kerf. Tungsten carbide-tipped saw blades were introduced to extend the use of the blade between sharpening. The geometry of maximizing the output. from particular logs has been addressed since the late 1960's. This work continues today, incorporating ever more sophisticated computer and laser techniques to maximize output per log.

2 Supply and Demand in the Lumber Market

Our development of the supply function is based on a Cobb- Douglas production function as suggested by Griliches (1979).6 The ultimate specification of the supply and demand system (hence the Cobb-Douglas function) is supported by a Hausmain test (Hausman, 1978) reported below. As in Seldon (19871, the production function at time t is

where Q is the quantity produced, e is the base of natural logarithms, 8 is the rate of disembodied technical change, L is labor services, K is capital services, and

I

3 = n(G[i-4ZLi)a''" ; & 2 O , k , 2 0 i+,

6 R&D. See, for instance, J&e (19861, Griliches (19861, and Suzuki (1985).

The Cobb-Douglas production function remains very useful in studies of

THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 243

is the accumulated research effect, where G is government R&D effort and 2 is private R&D effort by the suppliers of the final product. The coefficient h is inversely related to the depreciation rate R&D: the smaller is h, for instance, the faster research results become obsolete due to later breakthroughs. The lag on the initial private R&D effect is denoted as i,. This private R&D lag can be no longer than the lag on the initial public R&D effect because private industry has a shorter payback period than government due to competitive forces. Let the difference between the public and private R&D lags be k, 2 0. Then the lag on the initial public R&D effect is denoted as i, + k,.

FPL personnel inform us that, except for a few of the largest firms, the sawmill industry does very little of its own research. Basic R&D is performed by the government and the results are turned over to the industry's equipment suppliers which engage in the applied R&D necessary to operationalize the results. These intermediate firms develop the product and then market it. The industry simply buys new technology when they buy replacement parts or new capital equipment. Applied R&D performed by the intermediate firms is not part of the supply and demand system for softwood lumber. In preliminary regression equations which included a proxy for lumber firms' R&D similar to the one used in Seldon (19811, the associated coefficient was statistically insignificant and often took the incorrect sign. Therefore, we deleted the term and, to simplify our derivation for the present, we let 2,-i = 0. Then the technology term becomes

J=J0

We assume that the firms are competitive profit maximizers so that the industry as a whole solves the problem

max Q = P,Q(L, , K , . Y,) - Y L , - R,K, L, .K,

where n is profit; P is the price of the good, which the industry treats as exogenous; Q (t,K,Y,) is the Cobb-Douglas function; L, K, and Y are defined as above; and W and R are the wage rate and cost of capital. Substituting the technology term into the production function and the production function into the profit equation yields a distributed lag form of the industry supply equation'

7 This assumes equilibrium in each period, so the maximum profit is zero. Our supply function is exactly equation (7) of Seldon (1987) with the proxy terms for private R&D omitted since the firms are assumed not to engage in R&D.

B. SELDON & W.F. HYDE 244 ._ -

y = ( l - a - / 3 ) - ' . ( lb)

t is time; and q, p, w, r, andg are the natural logarithms of quantity of softwood lumber (Q), the price of softwood lumber (PI, the wage rate (W), the cost of capital (R) , and government :scientist months employed in softwood lumber research (G). All coefficients in the supply equation are expected to be positive.

The demand for softwood lumber arises mainly as a derived demand from construction companies and hardware stores," and our demand function reflects this. The log-linear demand function is

where q and p are defined as before, h i s the natural log of housing starts, p, is the natural log of the real price of related goods used in construction, and qA is the natural log of an index d hardware store sales in real terms.g We expect 6, (the own price elasticity) to be negative and 6, and 6, to be positive. The sign of6, depends upon whether the related goods are, on net, 21 substitute or complement.

8 Most softwood lumber is used by construction companies. For instance, in both 1962 and 1970 new housing and residential construction accounted for about four times as much lumber (of which more than 80 percent was softwood) as residential upkeep and improvements. The latter contains lumber sold by hardware stores as well as lumber sold to lmilding contractors (US. Department of Agnculture Forest Service, 1974, p. 181). 9 This demand is derived fmm the supply side of the construction and hardware retail markets, and excludes variables which. enter the demand side of the downstream markets. For instance, we exclude real income, which increases demand for (and hence is correlated with) construction and hardware sales. Therefore, the other estimated coeficit!nts in the demand equation would be inefficient if real income were included. We initially tried an alternative demand function similar to Seldon (1987) which included prices of outputs and costs of inputs to the downstream industries as argu- ments. This alternative function encountered severe convergence problems.

THE PRODUCTIVITY AND WELFARE EFFECTS OF C O V E R " R&D 245

3 Econometric Results

We have consistent records of government research effort in R&D for the period 1950-80. We estimate the supply and demand system using nonlinear three stage least squares (NL3SLS) applied to equations (1) and (21, with A and y in (1) replaced by equations (la) and (lb). The data are described in Appendix A

The supply and demand system yields the best fit in terms of correct signs and significance levels when government R&D is lagged five years.'O This implies that government R&D conducted in period t will not affect output until period t+5. This does not seem unreasonable given the large number, small size, and diffuse location patterns of sawmills and the competitive nature of the industry." Since most sawmills do not engage in applied R&D, the basic R&D results of the FPL are refined by firms which supply the industry, and it takes some time for these suppliers to develop fhe products and market them. Furthermore, even for government R&D which did not require new equipment for implementation by the firms,= it is plausible that the lag would be lengthier than in other manufacturing industries since diffusion would be slower with the larger number of firms. It would then take additional time for the mills to experiment with the new techniques.

The time variable in equation (11, which is a proxy for disembodied technical change, was extremely insignificant and was subsequently excluded. As mentioned previously, we have also excluded a proxy for the sawmill industry's own R&D. If either exclusion leads to misspecification, the Hausman test would reject

10 We tried lags ranging from one year to ten years. Except for the system where the lag was five years, the results indicated theoretically incorrect signs (e.g., positive price elasticities of demand and/or negative output elasticities for labor or capital), and/or explosive values for A (viz. A > l), and or low significance levels for the various coefficients. 11 The industry is quite competitive. For example, in 1977 there were 6,802 companies with 7,544 plants (many companies are single mill operations, 50 entry costs are low) and the four firm concentration ratio was 17 percent (Census ofManufactures). The R&D lag that we find is somewhat longer than for manufacturing industries in general where the lags tend to be around 2 years (Pakes and Schankerman, 1984). 12 Examples include lumber sizing and early studies of the geometry of cutting logs to achieve best yields which required *look-up tables, for the sawyer to consult.

B. SELDON & W.F. HYDE 246

the resulting supply and demand system. Omitting the time variable from equation (1) yields

qt = (1- I ) l n A + y ( a + p ) ( p , p ( w f - b t - 1 )

-$(q - b t - 1 ) + mi-5 + kt-1+ &s,t (3)

where A and y are defined by equations (la) and (1,) and where E , , ~ is the error term.

The demand and supply system composed of equations (2) and (3) was estimated and then tested for specification error using a Hausman test statistic rn=&'i where 4 is a column vector with elements equal to the difference between NL2SLS and NL3SLS estimates of the system coefficients and is the ma.trix of differences between the covariance matrices multiplied by tlhe inverse of the number of data points (Hausman, 1978). In our case, the scalar m is tested as a x2 statistic with 9 degrees offreedom. The null hypothesis is that the model is correctly specified. We calculate m = 1.31 which is extremely insignificant.l3 Hence we do not reject thle hypothesis that our system is correctly specified. This supports our exclusion of lagged total revenue and time.

Table 1 presents the econometric results. All coefficients in the supply equation take their expected signs and all are significant a t the 5 percent level or better." The estimated output elasticities for labor and capital are 0.17 and 0.08 respectively. T h e estimated output

elasticity for government R&D is Aip = p / (1-- A) = 0.92 with t

value = 2.06, significant at the 5 percent l8 The estimated price

04

i=O

13 The critical value a t the 5 percent level is 16.919. 14 One-tailed t tests are appropriate since the expected signs of all coefficients except 6 are unambiguous. 15 This R&b output elasticity takes .into consideration all effective government R&D. In the lumber case, this is all governiment R&D lagged 5 years and more. Specifically, the output elasticity of government R&D is (a, I 6G,-,) (GI-& I Q,> + (W, I sC,-J (GI-# I QJ + (W, I sC:,-,) (GI- , I 8,) + ... Since Q, = L . ~ K , b I l , ? s C ~ ~ we may write the summation as ,d5-5 + pP-5 +

OD + ... = z k i p = p / ( l - L ) . i = O

16 The standard deviation of a nonlinear function, f , of the vector of variables x is (( Syr ! 6rr) Z (Syr / &)')''' where Z is the covariance matrix associated with x. This is used in obtaining t ratios for all nonlinear functions.

THE PR0I)UCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 247

elasticity of supply is (a + P,/(l- a- P, = 0.34 with standard deviation 0.10 and t value 3.28.

Comparing our supply price elasticity with previous estimates provides further confidence in our results. Lewandrowski (1989) made the most thorough assessment of lumber supply and demand known to us. Adams and Haynes (1980) built the best known multi- market model of the U.S. forestry sector. They find regional supply price elasticities in the ranges of 0.18 - 0.38 and 0.21 - 0.79, respectively. Our estimate falls within their narrow combined range.

In the demand equation, all coefficients for which we have a priori expectations take their expected signs and all are significant at the 10 percent level or better. The coefficient associated with related goods is negative, suggesting that the related goods (enumerated in Appendix A) are complements. This variable is significant only at the 20 percent level, but we do not exclude i t since theory dictates its presence. If it were excluded, our other coefficients could be biased. The estimated own price elasticity of demand is - 0.56 and is significant at the 10 percent level. Previous estimates of the demand price elasticity range widely, fiom - 0.08 (Mills and Manthy, 1974) to -0.91 (Rockel and Buongiorno, 1982). Our estimate lies between Lewandrowski (19891, with regional elasticities between - 0.27 and - 0.44, and Robinson (1974), with an estimate of - 0.87 for the entire US.

There is no evidence of serial correlation in the equations. The Durbin-Watson statistic associated with the demand equation is in the inconclusive region and Durbin's h statistic (Durbin, 1970) associated with the supply equation is insignificant." In addition, the Hausman tes t should indicate an incorrect specification if autocorrelation is present; but it does not.

In addition to the Hausman test, we performed another test to see if we have included all relevant inputs in the supply equation. The sum of the output elasticities should sum to 1 in probability, so we test the null hypothesis that a + p + p / (1 - A) - 1 = 0. Our estimate of the sum of the output elasticities is 1.18 with standard deviation 0.37, so we do not reject the null hypothesis that the sum of output elasticities is 1.

17 Durbin's h is the appropriate test for autocorrelation in the supply equation since it has a lagged endogenous variable. The statistic i s analogous to a t statistic associated with the autocorrelation coefficient and is tested as a standard normal deviate.


4 The Calculation of the Internal Rate of Return ( I R R )

In this section, we outline the estimation of the IRR and we present equations which arise in the context of the softwood lumber market. The estimation takes into consideration an initial impact of government research (conducted in time t ) on the supply equation (in time t + 5, given the R&D lag) followed, in subsequent periods, by an erosion of this effect due to the displacement of past research by more current research. For full details of calculating the IRR see Seldon (1987).

With the 5 period lag on government R&D, research in time t does not affect the market until time t+5. Thereafter, given an R&D level of G (the antilog ofg) in period t and holding all other variables, including previous R&D, at their levels at time t (in order to isolate the effect of R&D in time t ) , the supply arid demand system (equations (3) and (2) respectively) due to G in period t+5+j (i 2 0) may be written

Q I + s + j = S I GaZLJ I C ' s + j (4)

and Ql+s+] = DIP,;bs+l ( 5 )

where In(S,) and ln(D,) include the intercepts and other predetermined variables of the log linear supply and demand system at time t," a, = (a+ / (1 - a-P> is the elasticity of supply, u2 = 7~ and -b = 6, < 0 is the elasticity of demand. Equations (4) imd ( 5 ) determine the equilibrium future price P in the (t + j + 51th period to be

E pG-m2aj

where o = (b + ~ ~ 1 - l . Seldon (1987) shows that the present values of consumer surplus and producer surplus (PVa and PV') due to R&D in period t are:

P,+S+, = I I

- PV; = (1 - b)-' P,Ql (1 + p)-' (1 - Gp'-' )

1=5 - and PKp8 = ( l - a , ) - ' P , Q , C ( l + p ) - ' ( G ~ * ' - ~ - 1)

1=6

18 excluding the variablesg,4, pr, and their associated parameters 80 that In@) = (1- U l n A + y ( a + B ) ( - Q t - l ) - W q - h t - 1 ) - @ C r l - %-I) + ht-1+ %,t

and h(Dl = 60 + 62hl + 63~ , ,1 + 6,qh,, + Ed.1

In other words, ln(S,) and ln(D,) may be written as equations (3) and (2)


where p is a time discount rate, s = -a2(l - b ) 0, and o = 5, These terms must be approximated by limiting the summations to the finite number of periods before the R&D contribution of the tth period has depreciated such that the future supply equation is close to the original supply equation. Using the variables and estimated parameters, we found that this occurred at 15 periods. Benefit to the economy as a whole is the sum PV,cs +PV,". Net benefits are commonly measured either in terms of consumer surplus or in terms of consumer and producer surplus. Subtracting R&D expenditures, El, from P V," and PV," + PV," gives the net present value of R&D in

each period.lB Then summing over the discounted terms (PV," - E l )

and (PVl" + PVtp - E l ) for the years 1950-80 gives the net present value of the entire 31-year research program in terms of either consumers only or consumers and producers. We calculate

30 and NPVneb = c(l+p)-t(Pv;" + PKp - E f )

f =o (7)

where NPV" and NPVMb are the net present values of the research program to consumers only and to both consumers and producers, respectively. The Z R R in terms of consumer surplus (IRE') is the value of p which equates equation (6) to zero. Similarly, the IRR for both consumers and producers (IRRnb) is the value of p which equates equation (7) to zero.

5 The Value of the Marginal Product and the Marginal Internal Rate of Return (MZRR)

Since the seminal work of Griliches (19641, the estimation of a production function has been used to calculate the value of the marginal product (VMP) of R&D investment and the associated MZRK20 The MIRR of R&D investment is calculated from estimates of the

19 20 the benefits of R&D occur in one year.

We address the estimation of the E series below. The calculation in Griljches (1964) is based on the assumption that all

260 B. SELDON Kt W.F. HYDE

VMP, although various studies treat details somewhat differently.*l We develop an MZRR which is consistent with the calculation of the I R R outlined above. We can do so because our econometric model estimated the production function parameters directly. Then we can compare the ZRR and the MZRR and, in turn, comment on the optimality of the ZRR.

Our development of the calculation of the VMP of R&D expenditures requires one more step than usual. This is because we use scientist-months in the production function instead of expenditures, which are, after all, just a proxy for R&D inputs. Specifically, we will need an expression for sQIEE, the change in output due to a change in R&D expenditures. From the Cobb-Douglas function, we have an expression for (@I 6G). Now R&D expenditures (E) are a function of government scientist months ((GI so E = EfG). In fact, E(G), = C,G,, where C, is the average cost of a scientist month in period t. Therefore, 6E,l6GI = C,. Since 6Eld;G exists and is nondecreasing, (SEISG)-’ = 6GI6E is well definedl and we see that 6G1/6E, = l / C , Since 6QI6E = (6QlSG) fGG/SE), we get

SQlSE = (1 I C ) (6QIE). (8)

While the VMP of R&D expenditures may be treated much the same as the VMP of any other input for any single period, the effects of R&D last into the future. Therefore, the appropriately discounted effects must be summed. To develop this idea, consider the effect of R&D at time t upon the output in period t+5 only. By our estimate, this is the first period that the R&D affects lumber output. We call this one-period effect VMP, in order ta distinguish, i t from the W P we ultimately develop. Using equation (8), the VMP of R&D expenditures E for the fifth period forward is

which is a discounted version of the usual definition of the value of the marginal product. With the Cobb-Douglas function specified above, we may substitute for SQ, + ,/SG, to obtain

21 notes the differences. Suzuki (1985) uses still another variant.

Davis (1981) compares calculations of MZRR across various studies and


Similarly, for any period t+5+rn, rn 2 0,

where the Am accounts for R&D depreciation. To isolate the effect of the research of time t from other demand-shifting factors operating between time t and t+5+rn, we replace the future total revenue in the last equation with current total revenue. Then, summing these single period returns, we get the value of the marginal product of R&D expenditures at time t

Thus we can estimate a V M P for each period of our sample.

However, since the early studies of Griliches (1964) and Peterson (1967) it has been the practice to report the geometric mean of the VMPs for each period to obtain a measure of the V M P of research. The geometric mean is used because it places less weight on extreme values than the arithmetic mean. The MIRE is the value of p which equates the geometric mean of equation (9) to unity, since the marginal cost of one dollar of R&D is, in fact, one dollar. This conforms exactly to the more general form of the MIRR given in Davis' survey article (1981, p. 64) since the weights we associate with periods earlier than the fifth period are zero.

6 TheCostofR&D

Expenditures on R&D are often the most difficult data to obtain, especially in studies at a disaggregated level. We are interested in the returns to estimates of all expenditures occasioned by government R&D. This includes both the direct cost to the FPL and associated agencies and the cost to the private firms of implementing the government While we are fortunate to have records of government R&D efforts, the implementation costs to the private firms must be estimated. Since this estimate is subject to error, we

22 We ignore the benefits and costs (hence profits) of the firms which supply equipment to the sawmill industry. Our estimates of returns research will be conservative if their profits are positive.


develop alternative ulowm and .high* estimates in order to give a range in which the true returns to research are likely to fall.

We suppose that each dollar of government expenditure necessitates an expenditure of n dollars per plant by the private firms and add this to the direct cost to the government. Then the total expenditure El may be expressed as

(10) where N, is the number of mills at time t! and c, is the direct cost to the government of a scientist month. Thus, C, of equation (8) equals

The direct cost to the government, c,, is constructed using an academic R&D price index from Sonka and Padberg (1979) and the estimated cos t of a USDA scientist year for 1977 from Callaham( 19811, and then adding overhead cost estimates supplied by the FPL. The result is deflated to 1967 dollars. N, is from various issues of the Census of Manufactures Industry Series with linear interpolations for missing years.

Obtaining the value for n (the imp'lementation cost per plant for every dollar of government research) is the most dificult part of the analysis. Cost of implementation data me unavailable for many FPL R&D projects in general and for softwood lumber research in particular. We were able to obtain an estimate of the average cost for a plant to adopt technology developed as a result of' a particular FPL R&D project used in sawmills (the original .Best Open Facen (BOF) project). Adopting this technology probably required higher expenditures than adopting many other new sawmill technologies. Therefore, the BOF project yields a high estimate of n and conservative final estimates of returns to research. Appendix B explains the calculation of n. Adoption of the BOF technology could cost a range of prices depending upon the configuration and sophistication of the equipment used in a particular plant. We estimate an average cost per plant and also establish lower and higher estimates corresponding to alternative assumptions that all plants use the least costly and most costly configurations, respectively. Dividing each of these three costs by the direct FPL cost of the project yields three values for n: $0.03, $0.09, and $0.29. These per-plant, per-government-dollar costs are lower tlhan the values in the plywood study (Seldon, 19871, which were $0.13, $0.26, and $0.39, but in every year there were many more softwood lumber mills than there were softwood plywood plants ( e g , 10,271 sawmills versus 180 plymills in 1967).

E, = (1 + dVJ (!,GI ,

(1 + nNJ c,.

THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 253 -~

Inserting the values ofNP cb Gb and n into equation (10) results in three alternative series for E,. Table I1 presents these series rounded to millions of 1967 dollars.

7- Returns to Government Research, 1950-80

Printing out intermediate steps in our calculation of the ZRRs, we found that the gross benefit to producers was negative in every year. This occurs because the transfers from producer to consumer surplus, which occur as a result of the lower price and higher quantity (and which represent a loss to producers), outweigh gains to producer surplus which result from outward shifts of the supply curve. Gross benefits must be positive in terms of consumers alone or consumers and producers combined but, since the benefit to producers is negative, we would expect ZRR- to be greater than ZRRMb. Net benefits to consumers and to consumers and producers changed signs only once, so we are assured of unique values for ZRR- and ZRRMb for each value of n. Table I11 presents the internal rates of return. The ZRR" is 56 percent, 34 percent, and 17 percent for n values of 0.03, 0.09, and 0.29 respectively. The ZRRmb is 47 percent, 27 percent, and 13 percent, respectively.

Table IV presents VMPs for three prespecified discount rates and MZRRs for the three values of n. The discount rates used to calculate the VMPs are 4 percent, 7 percent, and 10 percent.= For the cases where n = $0.29 and the discount rates are 7 percent or 10 percent, the values of the marginal product of research expenditures are below $1.00 (the marginal cost), so the MZRR for n =$0.29 should be less than 7 (and therefore less than 10) percent. The MZRRs for n = 0.03, 0.09, and 0.29 are 30 percent, 15 percent, and 5 percent. The MZRR is lower than the IRR in all cases. Therefore, average returns were de~lining.~'

23 These are the discount rates used for project evaluation by the US. Forest Service, the Water Resources Council, and the Office of Management and Budget, respectively. 24 The IRR shows the rate of return per dollar; hence it is an average.

B. SE [DON & W.F. HYDE 254 -

8 Conclusion

The internal rates of return for public sawmill1 research range upward from the neighborhood of the acceptable pnivate opportunity cost of capital. They compare with the low-to-middle range of estimated returns for public investments in agricultural research (Ruttan, 1980) and they are substantially in excess of returns to other (non-R&D) US. Forest Service investments in either nonindustrial private forestry (see, for example, Boyd, 1984, and Boyd and Hyde, 1989, Ch. 2) or public forest timber management (Boyd and Hyde, 1989, Ch. 8).

Both average and marginal internal rates of return in sawmill research are less than the comparable measures for softwood plywood (Seldon, 1987). There may be three reasons for the differences: 1) The longer research-implementation lag (5 years for sawmills versus 2 years for plywood) implies larger discounting of ;sawmill research benefits. 2) The larger number of sawmills means greater private implementation costs. 3) Plywood research was a smaller scale activity and existed for a briefer time period, so it may have always been under close management scrutiny. In contrast, there was a larger expenditure of public funds on sawmill research which may have allowed greater researcher discretion. The ;sawmill research budget was more secure and the large number of sawmills (one in almost every U.S. Congressional District) may have ensured its political support.

Nevertheless, the returns to government research in softwood lumber are quite acceptable and adds to the evidence that government R&D is productive. The government sawmill research investment yielded net positive social gains, gains that would have been unavailable were society t o rely solely on private research.% However, since the marginal internal rate of return was lower than the (average) internal rate of return, the internal rate of return could have been higher with less research funding. The U.S. government was somewhat overinvested in softwood lumber research.

25 The government franchises its patents to any interested party at zero cost. When a private firm is granted a patent it is able to enjoy monopoly rents which are bounded only by the cost savings of the invention since the potential users of the new technology would pay up to that amount for the new technology. If the rents reached this limit, the price of the final good would not fall.

THE PRODUCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 255 ~-

Appendix A: The Data

The Bureau of Labor Statistics supplied an index for total output of the industry (SIC 2421) for the years 1958 through 1980 (Ed Henneberger, personal communication). The value of shipments (price times quantity) for SIC 2421 was obtained from various issues of the Census of Manufactures for 1950-80. The definition of SIC 2421 changed in 1958, but the Census of Manufactures provides value of shipments figures for that year under both the old and new definitions. The ratio of these figures is used to reconstmct the data for 1950-57 in terms of the new definition. Dividing the value of shipments for 1958-80 by the quantity index yields a nominal price series where the price corresponds exactly with the quantity units, although the precise unit of measurement in terms of board feet is undetermined. We extend the price series backwards to 1950 using an own-price index for lumber (Ulrich, 1983) and divide these prices into value of shipments to construct the quantity series for 1950-57. Prices are then deflated to 1967 dollars using the all commodities producer price index.

The wage rate for SIC 2421 for 1958-80 (US. Department of Labor, 1979 & 1983) is adjusted to 1967 prices. Missing years are estimated using a regression equation of real wages in SIC 2421 on real wages in SIC 242 and time. A real user cost of capital index for SIC 24 was provided by Wharton Econometrics.

We obtained data for government R&D effort in terms of government scientist and engineer person-months from records maintained by the FPL. From the perspective of this research, i t is fortunate that the reporting format was consistent for many years. The format changed considerably in the late 1970’s and early 1980’s, however, making it difficult to extend our series past 1980.

Housing starts are from Ulrich (1983). The index of hardware stores sales (with 1967=100) is constructed by dividing nominal total sales of hardware stores, from various issues of The Statistical Abstract of the United States, by the consumer price index to get quantity and then dividing quantity in each year by quantity in 1967. The price index for related goods is a Divisia index of real prices for concrete, structural steel, plywood and veneer, and gypsum from Ulrich (1983) with weights for the various prices taken from input- output tables for the US. The weights for unreported years are interpolated.

B. SELDON & W.F. HYDE 256 -.

Appendix B: The Private Cost of Implementing Government R&D

In calculating the cost of implementing government R&D, we use an estimate of private costs of adoption of best opening face (BOF) equipment by the sawmills. This new technology emerged from an idea originated by Hiram Hallock, of the FF’L, for developing a computer program to determine the optimal approach to cutting particular logs. David Lewis, also of the FPL, worked on the BOF computer program to solve the log cutting problem after first having spent a few months developing the idea with Hallock. Their original discussions took place around 1969. Lewis (personal communication) repoh; that 39 scientist- months were spent on the project before their results were turned over to private firms (which supply the sawmills) for development in 1973. Since the FPL was engaged in this work over the period 1969-73, we use the midpoint year (1971) cost of F&D and estimate the direct cost to the FPL to be around $272,000 in 1967 dollars.

We assume that costs incurred b,y private intermediate firms were a t least covered by their revenues from equipment sales so we do not consider these costs. The adoption of BOF by sawmills required new scanning and process control technologies and new setting equipment. Jeanne Danielson of the FPL (personal communication) reports that currently about 50 percent of sawmills use some aspect of BOF, ranging from tables which determine the best opening face to computer, setting, or scanning equipment. The rainge of the cost of implementation is between $50,000 to $500,000 (current dollars) depending on the sophistication of the machinery, but the distribution is bimodal, with one mode between $50,000-$7ti,000 and another a round $250,000. We use three es t imates of t h e cost of implementation. The low and high cost estimates are $50,000 and $500,000. The middle cost is the mean of a probability distribution with 1/2 of mass distributed uniformly over $50,000-$75,000 and 1/2 of the mass at $250,000. In 1967 dollars, this translates to an induced cost to sawmills (per government dollar) of $0.06,$0.18, and $0.58. However, since only half of the existing sawmills use the new technology, we take half of these costs induced costs as the multiplier, so n is assumed to be $0.03, $0.09, or $0.29. Given the large number of plants in the industry (for instance, 10,016 in 1967 according to the 1982 Census of Manufactures) and the commitment of the FPL to sawmill research (ranging from 22 scientist months in 1961 to 129 in 1975) we derive total cost estimates that greatly exceed the case of softwood plywood (Seldon, 1987). These estimates are reported in Table 11.

THE PR0I)UCTIVITY AND WELFARE EFFECTS OF GOVERNMENT R&D 267

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260 B. SELDON & W.F. HYDE

Table I NL3SLS Estimates of Demand and Supply Coefficients

for Sawmills and Planing Mills

Demand Supply

0.1 727 * * (0.0741 )

0.0792 *** ( 0.0298 )

0.0256 ** ( 0.0148 )

0.9723 '** ( 0.0229 )

own price (6,)

housing starts (6,)

related goods price (6,)

hardware stores sales (6,)

11.1423 *** ( 4.2983 )

- 0.5562 ( 0.3879 )

0.2902 * * ( 0.1434 )

- 0.0770 ( 0.0716 )

0.5185 * * ( 0.2409 )

R2 .67 +

Durbin's h 0.239 Durbin-Watson -

.73 ' -

1.307

Degrees of 22 21 Freedom

Note: Standard errors are in parentheses.

** ***

t This is the usual Rz, but there are problems with any goodness of fit measure in simultaneous systems. See Judge eta/. (1 980, pp. 256-7).

Significant at the 10% level in a one-tailed test Significant at the 5% level in a one-tailed test Significant at the 1% level in a one-tailed test


Table II. Total Cost of Public Research in Sawmills, 1950-80 (Direct cost plus cost

of adoption, in millions of 1967 dollars)

Cost with Cost with Cost with Year n = 0.03 n a 0.09 n = 0.29

1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964

$1 69 156 176 169 166 161 102 102 98 86 72 52 53 79 75

965 95 966 82 967 93 968 65 969 109 970 88 971 113 1972 1973 1974 1975 1976 1977 1978 19'79 1980

98 125 93 193 166 151 119 137 109

$505 468 527 505 497 482 306 305 293 257 216 156 158 236 226

$1,627 1,506 1,697 1,627 1,599 1,551 984 982 945 826 694 503 508 760 727

284 91 4 245 787 279 899 194 626 327 1,053 264 85 1 339 1,090 294 375 280 578 497 452 357 41 1 326

947 1,206 900

1,861 1,601 1,456 1,148 1,323 1,049

262 B. SELDON & W.F. H M E

Table 111 Internal Rates of Return for Publlc Research lrivestment

In Sawmill Research, 1950-80

Value of n IRR" IRRnsb

0.03

0.09

0.29

56%

34%

17%

47%

27%

13%

Table IV Long Run Value of Marglnal Product and Marginal Internal Rate of

Return of Public Sawmill Investment, 1950-80 (All valules In 1967 dollars)

0.09 3.97 2.46 1.68 15%

I 5% 0.29 1.23 0.76 0.52 I

the productivity and welfare effects of government r\u0026d in the u.s. softwood lumber industry

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