Economics of Small Business

1. Economics of Small Business Drexel University Spring Quarter 2014 Fifth Week

2. Family Business1. Some Background

3. Small and Family Business • Not all small businesses are family businesses, and conversely. • However, there is an overlap, and family ownership and management are especially common in the smallest size range. • Accordingly, we will review some research on family businesses, which, in practice, are mostly SMEs.

4. Production Function • The reading for this week concerns the relative productivity of family SMEs • For present purposes, an SME is a firm with 200 or fewer employees. • The study uses a production function approach. • We begin with a bit of background on this.

5. Production Function 1 • We begin from the assumption that the output that a firm can produce is limited by the inputs it can command and the technology with which they can be used. • Given technology, generally more labor will result in more output, and more capital similarly will result in more output, both subject to diminishing returns.

6. Production Function 2 • Representing Q as output, L as labor input, and K as capital input, the production function would be Q=f(L,K) • This function is a mathematical rule that tells us how output increases or decreases when one or more of the inputs does. • The production function gives us the largest output that can be produced with the given inputs.

7. Some Math 1 • In practice we often use power functions and logarithmic functions to approximate f. • A power function is y=xa • A logarithmic function is calculated by a complex system of approximations (but computers are good at that.) • It can be written y=ln(x) or y= ln x • Well-known algebraic rules connect these two.

8. Some Math 2 • The rules tell us ln(xy)=ln(x)+ln(y) ln(x/y)=ln(x)-ln(y) ln(xa)=aln(x)

9. Cobb-Douglas 1 • Since the research of mathematician Charles Cobb and economist (later Senator) Paul Douglas, economists often use the Cobb-Douglas function to approximate the true production function, whatever it is. • The Cobb-Douglas function is • Here A is a constant that corresponds to overall or “total factor” productivity.

10. Cobb-Douglas 2 • Taking logarithms on both sides of the equation, we have the equivalent expression, • (It is conventional to leave off the parentheses.) • This linear function is useful for statistics!

11. Cobb-Douglas 3 • Without going into the mathematical details, if labor is paid its marginal product, then the wage is • So that the share of wages in product is

12. Terminology • The constants a and b are what the authors call the “productive contribution” of capital and labor respectively. • They can be estimated by a linear regression of lnQ on lnN and lnK – assuming that a and b both are constants for all the production units observed.

13. Simplifying Assumptions • In this we assume • That labor and capital each are homogenous quantities, • That land and raw materials are not important, so that in practice, Q is “value added,” that is, revenue minus the cost of raw and semifinished materials, • Everyone uses the same technology.

14. Family Firms • A family firm, for present purposes, is a SME (fewer than 200 employees) owned and controlled by a family. • There are several reasons to think that, even if they have the same quantities of inputs and the same technology, family firms might use them in different ways and thus produce either less or more.

15. Differences 1 • Family members benefit directly from increases in the productivity of the firm, and so may be more committed than non-family members, and family-member employees may work harder, increasing labor productivity. • This is described as “lower agency cost” since a non-family manager is an agent of the owners. • Family managers may lack professional training that a non-family manager might have.

16. Differences 2 • Family businesses may be more risk averse, since losses could deprive future generations of the family of its wealth. • They may avoid debt or leverage for the same reason. • Family managers may, however, have a more long-term perspective, for the same reason: future generations can benefit from decisions made today.

17. Differences 3 • Family managers, motivated by “nonpecuniary preferences,” may divert business resources to their own consumption. • Similarly, motivated by lifestyle preferences rather than money, they may not try to maximize profits but base their decisions on other, more personal reasons.

18. Statistical Approach 1 • How can we allow for these differences? • One way is as follows: we modify the Cobb-Douglas equation By adding a dummy variable D that is zero for a non-family firm and one for a family firm. • We need also to allow for a random error, of course!

19. Statistical Approach 2 • So now we have where e is a random error and g, a and b are estimated best fit coefficients, i.e. slopes.

20. Statistical Approach 3 • The reading expresses it a little differently, writing ln(Aij) for j=1 a family firm or j=0 a non-family firm and i a particular firm. That is where e is the random error in the observation of firm i. • Let us call this the “old approach.”

21. Statistical Approach 4 • But this contains a hidden assumption – namely that a and b, the “productive contributions,” are the same for both family and non-family firms. • The reading argues that they probably are not – and gives some reasons for that. • Thus, instead of the previous approach, the reading introduces two dummy variables – say, D1 and D2.

22. Statistical Approach 5 • D1 and D2each is one for a family firm and zero for a non-family firm, as before. • However, D1 is multiplied by lnL and D2 by lnK. • Thus we now have

23. Statistical Approach 6 • In the language used in the reading, so the two dummy variables (technically known as interactive dummy variables) in effect allow for the slope coefficients to differ for j=1, family and j=0, nonfamily firms. • We will call this the “new approach.”

24. Data 1 • The data is on Australian firms for four years in the 1990’s. • Just over 3000 firms were observed. • Labor is measured as FTE employees. • K is measured as firm assets. • A questionnaire gives information on family or non-family organization.

25. Data 2 • “Output,” as noted before, is value-added. • Several other characteristics of the firms, “control variables,” are also used and are indicated as a vector (multidimensional) variable X. • The industry (dummy variable) and age of the firm could be important, so this allows us to take them into account.

26. Estimation 1 • The simplest and best known method for estimating slope variables is least squares regression. • However, in some economic applications, it can be biased, i.e. give wrong answers. • A standard way of correcting for this is “2-stage least squares,” (2SLS) also known as “instrument variables.”

27. Estimation 2 • I’m not going into details about 2SLS! • To be safe, the authors compute both the “ordinary” least squares estimates, OLS, and the 2-stage estimates. • They also check for differences by year and some other alternative approaches. • Bottom line: with one exception it makes no difference.

28. Estimation 3 • Since the year, 2SLS, etc, seem to make no difference we can skip down to Table 11, and focus on the OLS results. • LnA is the same for both family and non-family firms. That is, overall efficiency is about the same. • ai,j is almost ten percent larger. • bi,j is a quarter smaller.

29. Interpretation • Since ai,j is the “productive contribution” of labor and bi,j is the “productive contribution” of capital, we can say that family firms make more effective use of labor, which therefore has higher productivity; but less effective use of capital, which therefore has lower productivity.

30. Reliability • All the usual tests of statistical reliability indicate that these results are extremely reliable.

31. Exception • Looking at Table 10, where the authors check for differences by firm size, we find that this result is almost completely limited to firms with 10 or fewer employees. • (They are by far most of the firms observed, because of the skewness of the distribution of firm size.) • Thus we had best say that VSE family firms make better use of labor and less effective use of capital – This may not be applicable to SBs and MSEs.

32. Contrast • In any case, when the estimate is based on the “old approach,” the estimate is that lnA, the overall efficiency of family firms, is about 4% less. • This was also found in earlier research. • It now seems to be a mistake – a result of oversimplification. • The “old approach” estimates of the “productive contribution” of capital and labor are also in line with earlier research – which may therefore be unreliable.

33. Takeaways 1 • We have some reasons to think that family firms, especially in the VSE category, may make different use of inputs than non-family firms. • The Cobb-Douglas production function approach provides a way to test that, if we have the data. • We do now have sources of data on firms that we can put to work in statistical studies on this issue. • Earlier research suggests small firms may make less effective use of resources.

34. Takeaways 2 • But this earlier research is based on the simplifying assumption that the “productive contributions” of capital and labor are the same. • When we allow for differences in the “productive contributions,” the case appears more complex. • There seem to be no differences in overall efficiency. • Labor seems more effectively used. • Capital less so.