The process of hiring a professional dog walking service is not simply a transactional affair, akin to purchasing a loaf of bread. Rather, it is a critical decision that can have numerous implications for your pet's health, happiness, and overall quality of life. This assertion is not intended as hyperbole. Consider the following: the American Veterinary Medical Association (AVMA) indicates that dogs, depending on their size, age, and health, should get between 0.5 to 2 hours of exercise on an average day. Given our increasingly busy schedules, it is not always feasible for dog owners to meet these guidelines personally. Hence, the importance of a professional dog walking service becomes apparent.

To that end, think of employing a dog walking service as a complex amalgamation of economic behavior theory and social psychology, wrapped in a statistically-informed, decision-making process. Just as a prudent investor would not place their money in an unknown stock without thorough research and analysis, a pet owner should not entrust their beloved companion to anyone without doing due diligence.

Firstly, let's delve into the behavioral economic theory of information asymmetry, a concept that won George Akerlof, Michael Spence, and Joseph Stiglitz the Nobel Prize in Economics in 2001. In essence, this theory posits that in any transaction, one party often has more or better information than the other, which can result in an imbalance of power. When hiring a dog walking service, the service provider inherently knows more about their capabilities and reliability than the dog owner. This information asymmetry can be mitigated by conducting rigorous research, asking for references, and reading reviews.

Now, let's transition to the realm of social psychology. According to Robert Cialdini's Influence: The Psychology of Persuasion, people tend to place more value on services they pay for. This cognitive bias, known as the 'endowment effect,' might cause you to perceive a higher-priced dog walking service as inherently superior. However, cost does not always equate to quality and it is essential to weigh multiple factors in your decision-making process.

Turning to statistics, consider the Law of Large Numbers and its practical application in this context. According to this law, as the number of instances (in this case, dog walking services) increases, the average of the results obtained should be close to the expected value. Thus, by considering a large sample size of services, you are more likely to identify a suitable selection that aligns with your expectations.

As for where to hire these services, it's advisable to consider both online platforms and local businesses. Online platforms often provide the convenience of booking and payment options, and typically have review systems in place. However, local businesses may offer a more personalized service, potentially offering a deeper understanding of your community's specific needs and environment.

When it comes to the optimal timing of employing a dog walking service, it significantly depends on your dog’s daily routine and habits. Some dogs may require daytime walks while their owners are at work, while others may need an early morning or late evening walk due to their specific sleep and activity patterns.

Regarding the 'how,' begin by shortlisting potential services based on their reputation, range of services, and cost. Arrange meetings with your top choices to assess their compatibility with your dog. This step is essential as it allows for an evaluation of the walker's communication skills, patience, and passion - traits that don't necessarily correlate with their commercial reputation or price point.

In conclusion, hiring a professional dog walking service is a decision that should not be taken lightly. It requires thorough research, critical analysis, and careful consideration of several factors. By adopting a more intellectual approach and applying theories from economics, psychology, and statistics, you're more likely to find the ideal service for your beloved canine companion. After all, they deserve nothing but the best.