Big firms invest more, but a firm's good year is a weaker signal

Does a firm invest more in a year its market value rises? Each row is one firm-year: eleven large American companies from 1935 to 1954, with gross investment and market value in millions of 1947 dollars. Across the panel the answer looks like a resounding yes. Within one firm, from one year to the next, it is a quieter yes, and for some firms no answer at all.

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Across firms, size explains most of it

Each point is one firm-year, colored by firm, with a fitted line per firm. Across firm-year levels, market value and investment had correlation 0.862, but most of that is General Motors sitting far up and to the right of everyone else: its mean market value was $4,334 million, against $71 million for Diamond Match. The other ten firms crowd the bottom-left corner.

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Within a firm, the link is weaker

Replace each firm-year with its change from the firm's previous year. Size drops out, and what remains is whether a firm that gained value invested more. Across within-firm annual changes, the correlation was 0.562. The cloud leans the right way, but it is a cloud.

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IBM tracked its value; Diamond Match ignored it

One panel per firm, on log axes so that a $70 million firm and a $4 billion one each show their own twenty years. Inside IBM, market value and investment had correlation 0.975: twenty years on a line. Inside Diamond Match, the correlation was -0.096, a cloud with no lean at all. The pooled 0.86 is an average over eleven firms that range from lockstep to no relationship.

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Takeaway

Bigger firms invest more; that is the 0.86. Whether a firm's good year brings more investment is a different question, and the answer varies by firm from 0.98 to below zero. A pooled correlation on panel data answers the between question while sounding like the within one.

Limits

Eleven firms chosen in 1958 for a regression textbook, not a sample of industry. Twenty years per firm give each within-firm correlation only nineteen changes. The dollars are deflated to 1947 but not adjusted for the firms' very different capital stocks.