Appendix F: Robustness Checks Using Staggered Difference-in-difference-in-difference | RDP 2023-10: Adoption of Emerging Digital General-purpose Technologies: Determinants and Effects

RDP 2023-10: Adoption of Emerging Digital General-purpose Technologies: Determinants and Effects Appendix F: Robustness Checks Using Staggered Difference-in-difference-in-difference

Kim Nguyen and Jonathan Hambur

December 2023

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We also employ a staggered difference-in-difference-in-difference framework where we interact the treatment variable and the group split. This approach is very similar to the event studies but allows for easier testing of differences in outcomes between groups.

\begin{array}{l} y_{i, t} = α + \sum_{h} β_{h} 1 {T r e a t = h} + \sum_{g} γ_{g} 1 {G r o u p = g} + \sum_{h} \sum_{g} ω_{h, g} 1 {T r e a t = h} * 1 {G r o u p = g} \\ + μ_{i} + {X^{'}}_{i, t} Γ + θ_{s} + \sum_{g} η_{g} 1 {G r o u p = g} * ({X^{'}}_{i, t} + θ_{s}) + ε_{i, t} \end{array}

where:

h = {\begin{array}{l} 0 if t \leq A d o p t_{i} - 2 \\ 1 if t = A d o p t_{i} O R t = A d o p t_{i} - 1 \\ 2 if t = A d o p t_{i} + 1 \\ 3 if t = A d o p t_{i} + 2 \\ 4 if t = A d o p t_{i} + 3 \end{array}

Firms are split into groups g based on their characteristics of interest (having a Board member with GPT background, having a female Board member, early or late or non-adopters). Our coefficients of interest are $ω_{h, g}$ which trace the difference in profitability of firms in group g between post-adoption and pre-adoption periods, relative to the control group. We start the GPT and female regressions in 2015 and the late versus early adoption regression in 2011 given we do not model longer lags so have less need for prior information.^[18]

Results shown in Table F1 confirm the event study findings that suggest the role of GPT background and female representation on the Board for firm profitability following adoption. Similarly, there is a significant difference between outcomes for early and late adopters post-adoption.

Table F1: Difference in Post-adoption Outcomes by Firm, Board and Period
Using staggered difference-in-difference-in difference, relative to alternate cohort
	Firms with GPT experience	Firms with female representation	Late adopters
At adoption	−1.798 (2.142)	2.062 (1.773)	3.880 (3.223)
Post-adoption
One year	3.430 (3.334)	5.222** (2.526)	4.496 (3.101)
Two years	7.098* (3.951)	0.244 (2.937)	5.606* (3.304)
Three years plus	1.671 (4.890)	3.106 (3.285)	5.924 (3.187)
Number of observations	7,555	7,555	11,598
Notes: Firms in the IT sector are excluded. , , ** indicate significance at the 10, 5 and 1 per cent level, respectively. Standard errors are shown in parentheses and are clustered at the firm level. Sources: Authors' calculations; Morningstar; Refinitiv; S&P Capital IQ.

Footnote

Results are quite similar if we match the earlier specification periods exactly. However, we preferred this sample given the pooling of past periods in this specification. [18]