Machine learning approaches to understand IT outsourcing portfolios

Abstract

The outsourcing of IT services poses a conundrum to the traditional theories of the firm. While there are many prescriptive sourcing metrics that are geared towards the evaluation of tangible and measurable aspects of vendors and clients, much of the information that is traditionally important in making such decisions is unstructured. To address this challenge, we train and apply our own NLP model based on deep learning methods using doc2vec, which allows users to create semi-supervised methods for representation of words. We find two novel constructs, vendor–client alignment and vendor–task alignment, that shape partner selection and the alternatives faced by clients in IT outsourcing, as opposed to agency or transaction cost considerations alone. Our method suggests that NLP and machine learning approaches provide additional insight, over and above traditionally understood variables in academic literature and trade and industry press, about the difficult-to-elicit aspects of vendor–client interaction.

Appendices

Appendix 1: MCMC inference for hierarchical bayesian model

In this Appendix, we describe estimation details of the multinomial logistic regression with unobserved heterogeneity using the MCMC approach. As the MCMC approach involves iteratively updating values of parameters, we use superscript $n$ to represent the parameter values in the next iteration.

Step 1: Generating ${{\varvec{\beta}}}^{n}$, the coefficients in the multinomial logistic model that are homogenous across firms.

$$ {\varvec{\beta}}^{n} |{\varvec{\beta}}, c_{i}^{{}} ,v_{j}^{{}} , d_{ij}^{{}} , data $$

$$ f\left( {{\varvec{\beta}}^{n} {|}{\varvec{\beta}}, c_{i}^{{}} ,v_{j}^{{}} , d_{ij}^{{}} , data} \right) $$

$$ \propto \left| {{\Sigma }_{{{\varvec{\beta}}0}} } \right|^{{ - \frac{1}{2}}} exp\left[ { - \frac{1}{2}\left( {{\varvec{\beta}}^{n} - \overline{{{\varvec{\beta}}_{0} }} } \right)^{^{\prime}} {\Sigma }_{{{\varvec{\beta}}0}}^{ - 1} \left( {{\varvec{\beta}}^{n} - \overline{{{\varvec{\beta}}_{0} }} } \right)} \right]L\left( Y \right) $$

Here ${\varvec{\beta}}=[{{\varvec{\beta}}}^{{\varvec{c}}},{{\varvec{\beta}}}^{{\varvec{v}}},{{\varvec{\beta}}}^{{\varvec{d}}}]$, $\overline{{{\varvec{\beta}} }_{0}}$ and ${\Sigma }_{{\varvec{\beta}}0}$ are diffused priors, where we set $\overline{{{\varvec{\beta}} }_{0}}$ to be a vector of zeros and ${\Sigma }_{{\varvec{\beta}}0}=30I$. The Metropolis–Hasting algorithm is employed to randomly draw ${{\varvec{\beta}}}^{d}$ for the new iteration from the conditional distribution described in the equation above. The probability of accepting the newly drawn vector ${{\varvec{\beta}}}^{d}$ is calculated as:

$$ \Pr \left( {\text{accept new value}} \right) = {\text{min}}\left\{ {\frac{{{\text{exp}}\left[ { - \frac{1}{2}\left( {{\varvec{\beta}}^{d} - \overline{{{\varvec{\beta}}_{0} }} } \right)^{^{\prime}} {\Sigma }_{{{\varvec{\beta}}0}}^{ - 1} \left( {{\varvec{\beta}}^{d} - \overline{{{\varvec{\beta}}_{0} }} } \right)} \right]L(Y|{\varvec{\beta}}^{d} )}}{{{\text{xp}}\left[ { - \frac{1}{2}\left( {{\varvec{\beta}} - \overline{{{\varvec{\beta}}_{0} }} } \right)^{^{\prime}} {\Sigma }_{{{\varvec{\beta}}0}}^{ - 1} \left( {{\varvec{\beta}} - \overline{{{\varvec{\beta}}_{0} }} } \right)} \right]L(Y|{\varvec{\beta}})}},1} \right\} $$

If the newly drawn vector is accepted, we then assign ${{\varvec{\beta}}}^{n}={{\varvec{\beta}}}^{d}$.

Step 2: Generating ${c}_{i}^{n},{v}_{j}^{n}$, unobserved terms for client and vendor firm respectively.

$$ f\left( {c_{i}^{n} {|}{\varvec{\beta}}^{n} , c_{i}^{{}} ,v_{j}^{{}} , d_{ij}^{{}} , data} \right) $$

$$ \propto \sigma_{c}^{ - 1} exp\left[ { - \frac{1}{2}\left( {c_{i}^{n} } \right)^{2} \sigma_{c}^{ - 1} } \right]L\left( Y \right) $$

$$ f\left( {v_{j}^{n} {|}{\varvec{\beta}}^{n} , c_{i}^{{}} ,v_{j}^{{}} , d_{ij}^{{}} , data} \right) $$

$$ \propto \sigma_{v}^{ - 1} exp\left[ { - \frac{1}{2}\left( {v_{j}^{n} } \right)^{2} \sigma_{v}^{ - 1} } \right]L\left( Y \right) $$

Here, the two $f(\bullet |\bullet )$ functions are posterior distributions. Intuitively, posterior distribution can be considered as a way to summarize your existing belief about certain distribution (prior distribution) and additional empirical data you observed (data). As a closed-form solution does not exist for the two equations above, we again use the Metropolis–Hasting algorithm to randomly draw from the conditional distribution specified above. We employ the method in Atchade (2006) to adaptively change the length of the steps in each iteration to help reduce the autocorrelation across MCMC iterations. The probabilities of accepting the newly drawn value for $c_{i}^{n} ,v_{j}^{n}$ are:

$$ \Pr \left( {\text{accept new value}} \right) = {\text{min}}\left\{ {\frac{{{\text{exp}}\left[ { - \frac{1}{2}\left( {c_{i}^{n} } \right)^{2} \sigma_{c}^{ - 1} } \right]L(Y|c_{i}^{n} )}}{{{\text{eexp}}\left[ { - \frac{1}{2}\left( {c_{i}^{{}} } \right)^{2} \sigma_{c}^{ - 1} } \right]L(Y|c_{i}^{{}} )}},1} \right\} $$

$$ \Pr \left( {\text{accept new value}} \right) = {\text{min}}\left\{ {\frac{{{\text{exp}}\left[ { - \frac{1}{2}\left( {v_{j}^{n} } \right)^{2} \sigma_{v}^{ - 1} } \right]L(Y|v_{j}^{n} )}}{{{\text{eexp}}\left[ { - \frac{1}{2}\left( {v_{j}^{{}} } \right)^{2} \sigma_{v}^{ - 1} } \right]L(Y|v_{j}^{{}} )}},1} \right\} $$

Step 3: Generating ${\sigma }_{c}^{n}$ and ${\sigma }_{v}^{n}$, the standard deviation of client and vendor unobserved terms.

The newly updated standard deviations for client- and vendor-specific unobserved terms are drawn from the distribution below:

$$ \sigma_{c}^{n} | c_{i}^{n} \sim IW\left( {7 + N,1 + \mathop \sum \limits_{i} \left( {c_{i}^{n} } \right)^{2} } \right) $$

$$ \sigma_{v}^{n} | v_{j}^{n} \sim IW\left( {7 + N,1 + \mathop \sum \limits_{i} \left( {v_{j}^{n} } \right)^{2} } \right) $$

Here we choose $7+N$, $1+{\sum }_{i}{({c}_{i}^{n})}^{2}$ and $1+{\sum }_{i}{({v}_{j}^{n})}^{2}$ as hyperparameters of these two distributions, as they generate better predictive performance compared with other potential values. Note that hyperparameters of a MCMC are parameters of the underlying distribution from which our model parameters are generated (i.e., ${\sigma }_{c}$ and ${\sigma }_{v}$). IW denotes an inverse-Wishart distribution. We chose inverse-Wishart distribution because it is the conjugate prior for the variance of a normal distribution (i.e., ${\sigma }_{c}$ and ${\sigma }_{v}$). This method allows us to easily simulate values of variance (i.e., ${\sigma }_{c}$ and ${\sigma }_{v}$) from a distribution with closed form, instead of using the Metropolis–Hasting algorithm in Step 2.

Step 4: Generating ${d}_{ij}^{n}$, unobserved dyad term.

$$ f\left( {d_{ij}^{n} {|}{\varvec{\beta}}^{n} , c_{i}^{n} ,v_{j}^{n} , d_{ij}^{{}} , data} \right) $$

$$ \propto \sigma_{d}^{ - 1} exp\left[ { - \frac{1}{2}\left( {d_{ij}^{n} } \right)^{2} \sigma_{d}^{ - 1} } \right]L\left( Y \right) $$

Similar to client- and vendor-specific unobserved terms, we also use the Metropolis–Hasting algorithm to draw from the conditional distribution above. The method proposed by Atchade (2006) is used to adaptively change the length of step in each iteration. The probability of accepting a new value is:

$$ \Pr \left( {\text{accept new value}} \right) = {\text{min}}\left\{ {\frac{{{\text{exp}}\left[ { - \frac{1}{2}\left( {d_{ij}^{n} } \right)^{2} \sigma_{d}^{ - 1} } \right]L(Y|d_{ij}^{n} )}}{{{\text{eexp}}\left[ { - \frac{1}{2}\left( {d_{ij}^{{}} } \right)^{2} \sigma_{d}^{ - 1} } \right]L(Y|d_{ij}^{{}} )}},1} \right\} $$

Step 5: Generating ${\sigma }_{d}^{n}$, the standard deviation of dyad unobserved term.

Similar to Step 3, ${\sigma }_{d}^{n}$ can be drawn from the following distribution:

$$ \sigma_{d}^{n} | d_{ij}^{n} \sim IW\left( {1 + N\left( {N - 1} \right),1 + \mathop \sum \limits_{i} \mathop \sum \limits_{j} \left( {d_{ij}^{n} } \right)^{2} } \right) $$

Here we choose $1+N\left(N-1\right)$ and $1+{\sum }_{i}{\sum }_{j}{({d}_{ij}^{n})}^{2}$ as hyperparameters of this distribution, as they generate better predictive performance compared with other potential values. IW here also denotes an inverse-Wishart distribution.

Step 6: Go back to Step 1 if the estimation is not converged.

Appendix 2: Correlation matrix

See Table

Table 11 Correlation matrix

11.

Appendix 3: Robustness check with client firm characteristics

In our main model, we do not control for client and vendor firm characteristics, as many firms do not have historical firm-level data. In this robustness check, we include employee count and gross profits for clients who are publicly listed in North America. We present the estimation results in the tables below. As we can see, the results do not change significantly (Table

Table 12 Robustness check

12).

Appendix 4: An example of contract description in our dataset

Company A, a provider of Internet financial technologies and solutions, has awarded a 5-year technology support contract to Company B. Company A's technologies and solutions enable financial institutions to offer online financial services to their customers. Both companies expect this to be the start of an increasingly important business relationship in line with the growth of Internet banking in Europe. IDC estimates that this contract has a 5-year life and a value of $20–25 million. Contract Responsibilities: Through its relationship with Company A, Company B will provide desktop and server infrastructure support to Company C, to which Company A already provides Internet financial technologies, solutions, and Web hosting facilities. Company B will also work with Company A to assist Company C as it plans and implements its future technology strategy, including the management of other third-party information technology service providers. Company B will provide services and operate in Dublin. The services will include support operations onsite in Ireland, including servicing the UK, Germany and Singapore. This contract represents a key technology partnership for both Company B and Company A.